30-Progress\303\265es Estudo das Sequ\303\252ncias simples - progress\303\243o aritm\303\251tica, geom\303\251trica e outras - v\303\241rias propriedades e c\303\241lculos e gr\303\241ficos de Sequ\303\252ncias.

restart; GeoSum :=proc(a,N) local sum, k; sum := 0: for k from 0 to N do sum := sum + a(k); od: sum; end proc:

A id\303\251ia de uma seq\303\274\303\252ncia \303\251 uma lista de n\303\272meros. Por exemplo: O quadrado dos n\303\272meros naturais. k^2 $ k = 1..10;

NiwiIiIiIiUiIioiIzsiI0QiI08iI1wiI2siIyIpIiQrIg==

Podemos pensar nesses n\303\272meros como sendo o universo de uma fun\303\247\303\243o, cujo dom\303\255nio s\303\243o os n\303\272meros naturais. f := k -> k^2; array( [[ k,f(k) ] $ k = 1..10] );

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O 7\302\272 elemento de uma lista \303\251 f(7) e o 777\302\272 f(777); f(7); f(777);

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Geralmente, n\303\243o usamos a nota\303\247\303\243o padr\303\243o para fun\303\247\303\265es porque isso nos faz pensar em dom\303\255nios que incluem n\303\272meros n\303\243o naturais. Geralmente, representamos as Sequ\303\252ncias com letras . for k from 1 to 10 do a[k] = k^2; od;

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a[7] = f(7); a[77] = f(77);

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Defini\303\247\303\243o de Uma Progress\303\243o Aritm\303\251tica Uma progress\303\243o aritm\303\251tica \303\251 uma lista de n\303\272meros que t\303\252m entre si uma diferen\303\247a d comum. A sequ\303\252ncia inteira \303\251 determinada pelo valor inicial a[1] e a diferen\303\247a comum. k := 'k': a := 'a': a[k] := a[1] + d*(k-1);

NiM+JiUiYUc2IyUia0csJiYlImFHNiMiIiIiIiIqJiUiZEciIiIsJiUia0ciIiIiIiIhIiIiIiIiIiI=

Vejamos outros exemplos b := k -> 9 + 7*(k-1); b(k) $ k = 1..20;

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Se considerarmos a diferen\303\247a de quaisquer dois n\303\272meros consecutivos da seq\303\274\303\252ncia teremos a diferen\303\247a comum. b(4) - b(3); b(11) - b(10); b(100) - b(99);

NiMiIig=NiMiIig=NiMiIig=

c := k -> -11 + 5*(k-1); c(k) $ k = 1..20;

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c(4) - c(3); c(11) - c(10); c(100) - c(99);

NiMiIiY=NiMiIiY=NiMiIiY=

Talvez voc\303\252 reconhe\303\247a essas Sequ\303\252ncias aritm\303\251ticas comuns. b := k -> 1 + 2*(k-1); b(k) $ k = 1..20;

NiM+JSJiR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmIiIiISIiKiYiIiMiIiIlImtHIiIiIiIiNiI2IjYiNjYiIiIiIiQiIiYiIigiIioiIzYiIzgiIzoiIzwiIz4iI0AiI0IiI0QiI0YiI0giI0oiI0wiI04iI1AiI1I=

b := k -> 0 + 2*(k-1); b(k) $ k = 1..20;

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b := k -> 0 + 3*(k-1); b(k) $ k = 11..20;

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b := k -> 5 + 5*(k-1); b(k) $ k = 1..20;

NiM+JSJiR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwkKiYiIiYiIiIlImtHIiIiIiIiNiI2IjYiNjYiIiYiIzUiIzoiIz8iI0QiI0kiI04iI1MiI1giI10iI2IiI2ciI2wiI3EiI3YiIyEpIiMmKSIjISoiIyYqIiQrIg==

Encontrando o En\303\251simo Elemento \303\211 f\303\241cil encontrar qualquer termo da seq\303\274\303\252ncia se voc\303\252 souber a f\303\263rmula. J\303\241 que a f\303\263rmula \303\251 uma fun\303\247\303\243o, simplesmente resolvemos a fun\303\247\303\243o. a := k -> 100 + (k-1)*9;

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmIiMiKiIiIiomIiIqIiIiJSJrRyIiIiIiIjYiNiI2Ig==

`O 9\302\272 membro = `, a(9); `O 99\302\272 membro = `, a(99); `O 999\302\272 membro = `, a(999);

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Um problema comum \303\251 encontrar um determinado elemento SEM ter a f\303\263rmula. No entanto, podemos encontrar a f\303\263rmula facilmente se soubermos pelo menos dois elementos da seq\303\274\303\252ncia. Encontrando a F\303\263rmula Problema : Se uma progress\303\243o aritm\303\251tica come\303\247a 2, 9, 16, ... , encontre o 1000\302\272 elemento. Claramente a[0] = 2. Temos apenas que encontrar a diferen\303\247a comum. d = 9-2;

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Esta \303\251 a f\303\263rmula: a := k -> 2 + 7*(k-1);

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmIiImISIiKiYiIigiIiIlImtHIiIiIiIiNiI2IjYi

a(1000);

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Encontrando a Soma E assim encontramos a soma de uma s\303\251rie. a := k -> 16 + 9*(k-1);

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sum( a(k), k = 1..100);

NiMiJl1oJQ==

Encontrando o Valor M\303\251dio a := k -> 17 + 10*(k-1);

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmIiIoIiIiKiYiIzUiIiIlImtHIiIiIiIiNiI2IjYi

sum( a(k), k = 1..100); %/100;

NiMiJis3Jg==NiMiJDcm

Calculamos a soma e dividimos pelo n\303\272mero de elementos. No entanto, observe esses casos interessantes por onde tamb\303\251m encontramos a m\303\251dia. ( a(50) + a(51) ) /2;

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( a(1) + a(100) ) / 2;

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Parece que isso sempre funciona. Se voc\303\252 tirar a m\303\251dia da primeira e da \303\272ltima, \303\251 a m\303\251dia da seq\303\274\303\252ncia entre esses valores incluindo os pr\303\263prios. N := 1000; a := k -> 82 + 13*(k-1); sum( a(k), k = 1..N); %/N; ( a(1) + a(N) ) / 2;

NiM+JSJORyIlKzU=NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmIiNwIiIiKiYiIzgiIiIlImtHIiIiIiIiNiI2IjYiNiMiKCtiZCc=NiMjIiZeSiIiIiM=NiMjIiZeSiIiIiM=

N := 37145; a := k -> 52 + 29*(k-1); sum( a(k), k = 1..N); %/N; ( a(1) + a(N) ) / 2;

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Parece que funciona. Voc\303\252 pode provar?

Defini\303\247\303\243o de Uma Progress\303\243o Geom\303\251trica Uma progress\303\243o geom\303\251trica \303\251 uma lista de n\303\272meros que t\303\252m um quociente comum, r. A seq\303\274\303\252ncia inteira \303\251 determinada pelo valor inicial a e o quociente comum, r. (Geralmente Sequ\303\252ncias gepm\303\251tricas iniciam a sua indexa\303\247\303\243o em 0 em vez de 1, mas n\303\243o \303\251 uma regra.) k := 'k': a := 'a': a[k] := a*r^k;

NiM+JiUiYUc2IyUia0cqJiUiYUciIiIpJSJyRyUia0ciIiI=

Vejamos alguns exemplos b := k -> 100*(1/5)^k; b(k) $ k = 0..10;

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Se considerarmos o quociente de quaisquer dois n\303\272meros consecutivos da seq\303\274\303\252ncia, encontraremos o quociente comum, r. b(4)/b(3); b(11)/b(10); b(30)/b(29);

NiMjIiIiIiImNiMjIiIiIiImNiMjIiIiIiIm

b := k -> 64*(1/4)^k; b(k) $ k = 0..10;

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b(4)/b(3); b(11)/b(10); b(30)/b(29);

NiMjIiIiIiIlNiMjIiIiIiIlNiMjIiIiIiIl

Vejamos outras progress\303\265es geom\303\251tricas : b := k -> 1*(1/2)^k; b(k) $ k = 0..10;

NiM+JSJiR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IikjIiIiIiIjJSJrRzYiNiI2Ig==Ni0iIiIjRiMiIiMjRiMiIiUjRiMiIikjRiMiIzsjRiMiI0sjRiMiI2sjRiMiJEciI0YjIiRjIyNGIyIkNyYjRiMiJUM1

b := k -> 512*(1/2)^k; b(k) $ k = 0..15;

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b := k -> 12*(1/3)^k; b(k) $ k = 0..10;

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b := k -> 100*(.01)^k; b(k) $ k = 0..7;

NiM+JSJiR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwkKiYiJCsiIiIiKSQiIiIhIiMlImtHIiIiIiIiNiI2IjYiNiokIiQrIiIiISRGJCEiIyRGJCEiJSRGJCEiJyRGJCEiKSRGJCEjNSRGJCEjNyRGJCEjOQ==

Se 0 < r < 1, ent\303\243o a seq\303\274\303\252ncia geom\303\251trica descende em dire\303\247\303\243o ao zero bem rapidamente. Se r > 1, ent\303\243o a seq\303\274\303\252ncia cresce. b := k -> 1*(2)^k; b(k) $ k = 0..14;

NiM+JSJiR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IikiIiMlImtHNiI2IjYiNjEiIiIiIiMiIiUiIikiIzsiI0siI2siJEciIiRjIyIkNyYiJUM1IiVbPyIlJzQlIiUjPikiJiVROw==

b := k -> 100*(5/4)^k; b(k) $ k = 0..7;

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b := k -> .00319*(10)^k; b(k) $ k = 0..7;

NiM+JSJiR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwkKiYkIiQ+JCEiJiIiIikiIzUlImtHIiIiIiIiNiI2IjYiNiokIiQ+JCEiJiQiJSE+JEYlJCImKz4kRiUkIicrIT4kRiUkIigrKz4kRiUkIikrKyE+JEYlJCIqKysrPiRGJSQiKysrKyE+JEYl

Encontrando o En\303\251simo Elemento \303\211 f\303\241cil encontrar qualquer elemento da seq\303\274\303\252ncia se voc\303\252 souber a f\303\263rmula. J\303\241 que a f\303\263rmula \303\251 uma fun\303\247\303\243o, simplesmente resolvemos a fun\303\247\303\243o. a := k -> 999*(8/9)^k;

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwkKiYiJCoqKiIiIikjIiIpIiIqJSJrRyIiIiIiIjYiNiI2Ig==

`O 9\302\272 membro = `, a(5); `O 99\302\272 membro = `, a(10); `O 999\302\272 membro = `, a(20);

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Um problema comum \303\251 encontrar um determinado elemento da fun\303\247\303\243o sem ter a f\303\263rmula. No entanto, podemos facilmente encontrar a f\303\263rmula se soubermos pelo menos dois elementos da seq\303\274\303\252ncia. Encontrando a F\303\263rmula Problema : Se uma progress\303\243o geom\303\251trica come\303\247a com 20, 4, ... , encontre o 12\302\272 elemento (onde a[0]=20, a[1] = 4,...). Claramente a = 20. Precisamos apena encontrar o quociente comum. d = 4/20;

NiMvJSJkRyMiIiIiIiY=

Aqui est\303\241 a f\303\263rmula a := k -> 20*(1/5)^k;

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwkKiYiIz8iIiIpIyIiIiIiJiUia0ciIiIiIiI2IjYiNiI=

a(12);

NiMjIiIlIilEIkcpWw==

F\303\263rmula Para a Soma de S\303\251ries Geom\303\251tricas H\303\241 uma f\303\263rmula para as somas das s\303\251ries geom\303\251tricas. Vamos utilizar essa f\303\263rmula de uma maneira semelhante \303\240 prova. a:='a': b:='b': c:='c': a:= k -> c*r^k;

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiomJSJjRyIiIiklInJHJSJrRyIiIjYiNiI2Ig==

S := GeoSum( a, 10);

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r*S; expand(%);

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S - r*S: % = expand(%);

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S:= 'S'; S - r*S = c - c*r^11 ; S*(1 - r) = c*(1-r^11); S := c*(1-r^11)/(1 - r);

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Encontrando a Soma Isso nos leva \303\240 f\303\263rmula de s\303\251ries geom\303\251tricas finitas: S := (c, r, N) -> c*(1-r^(N+1))/(1-r);

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a := k -> 20*(1/5)^k; `Os primeiros 11 elementos = `, a(j) $ j = 0..10; `A soma dos primeiros 11 elementos = `,S(20, 1/5, 10);

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a := k -> 4*(1/2)^k; `Os primeiros 11 elementos = `, a(j) $ j = 0..10; `A soma dos primeiros 11 elementos = `,S(4, 1/2, 10);

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Somas Interessantes Este \303\251 um caso interessante. Se considerarmos uma progress\303\243o geom\303\251trica simples com a = 1 e r = 1/2 e as somarmos, teremos um n\303\272mero bem pr\303\263ximo de dois! a := k -> (1/2)^k; `Os primeiros 21 elementos = `, a(j) $ j = 0..20; `A soma dos primeiros 11 elementos = `,S(1, 1/2, 20); evalf(S(1, 1/2, 20));

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Voc\303\252 pode perceber mais algumas coincid\303\252ncias... ......... r = 1/2 ............ A soma \303\251 pr\303\263xima de 2 ......... r = 2/3 ............ A soma \303\251 pr\303\263xima de 3 ......... r = 3/4 ............ A soma \303\251 pr\303\263xima de 4 ......... r = 9/10 ............ A soma \303\251 pr\303\263xima de 9 a := k -> (2/3)^k; `Os primeiros 21 elementos = `, a(j) $ j = 0..20; `A soma dos primeiros 21 elementos = `,S(1, 2/3, 20); evalf(S(1, 2/3, 20));

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a := k -> (3/4)^k; `Os primeiros 21 elementos = `, a(j) $ j = 0..6; `A soma dos primeiros 21 elementos = `,S(1, 3/4, 20); evalf(S(1, 3/4, 20));

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Isso sai do padr\303\243o? a := k -> (9/10)^k; `Os primeiros elementos = `, a(j) $ j = 0..6; `A soma dos primeiros 11 elementos = `,evalf(S(1, 9/10, 10));

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`A soma dos primeiros 21 elementos = `,evalf(S(1, 9/10, 20));

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`A soma dos primeiros 31 elementos = `,evalf(S(1, 9/10, 30));

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`A soma dos primeiros 41 elementos = `,evalf(S(1, 9/10, 40));

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H\303\240 um n\303\272mero infinito de outras variedades de Sequ\303\252ncias. Aqui temos algumas. Perceba que algumas delas s\303\243o constit\303\272idas pela combina\303\247\303\243o de aritm\303\251tica, geometria, fatoriais, sinais alternados e outras opera\303\247\303\265es matem\303\241ticas para criar Sequ\303\252ncias ainda mais complexas. k := 'k': a := k -> (-1)^k; a(k) $ k = 1..20;

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a := k -> (-1)^(k+1); a(k) $ k = 1..20;

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a := k -> ((-1)^k)*2^k ; a(k) $ k = 1..15;

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a := k -> ((-1)^k)/3^k ; a(k) $ k = 1..10;

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a := k -> 1/k! ; a(k) $ k = 1..10;

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a := k -> (k^2)/k!; a(k) $ k = 1..10;

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a := k -> (k^2/2^k) ; a(k) $ k = 1..10;

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a := k -> (((-1)^k)*k^3)/k! ; a(k) $ k = 1..10;

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a := k -> ((-1)^k)/3^k ; a(k) $ k = 1..10;

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a := k -> 1/(k^2 + 1); a(k) $ k = 1..10;

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a := k -> 1/(k^3 + k!) ; a(k) $ k = 1..10;

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a := k -> lcm(k,k+3) ; a(k) $ k = 1..10;

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a := k -> floor( k/2) ; a(k) $ k = 1..20;

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a := k -> floor( floor( k/2)/3) ; a(k) $ k = 1..20;

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a := k -> k*2^floor( k/5) ; a(k) $ k = 1..20;

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a := k -> gcd(k, 4); 'gcd(k, 4)' $ k = 1..35;

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a := k -> gcd(k, k+5); 'gcd(k, k+5)' $ k = 1..35;

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a := k -> gcd(k, (k-1)!); 'gcd(k, (k-1)! )' $ k = 1..35;

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a := k -> gcd(k, (k-1)!); 'lcm( gcd(k,4), gcd(k,3) )' $ k = 1..40;

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2Ii0lJGdjZEc2JCUia0ctJSpmYWN0b3JpYWxHNiMsJiUia0ciIiIiIiIhIiI2IjYiNiI=NkoiIiIiIiMiIiQiIiVGIyIiJ0YjRiZGJUYkRiMiIzdGI0YkRiVGJkYjRidGI0YmRiVGJEYjRihGI0YkRiVGJkYjRidGI0YmRiVGJEYjRihGI0YkRiVGJg==

Progress\303\265es aritm\303\251ticas t\303\252m algumas similaridades nas linhas. Em ambos os casos, a quantidade de crescimento \303\251 constante independente da vari\303\241vel. E, como nas linhas, as progress\303\265es aritm\303\251ticas s\303\243o crescentes ou decrescentes dependendo do coeficiente ou da vari\303\241vel, que funciona como a inclina\303\247\303\243o. a := k -> 2*k - 3; a(k) $ k = 1..10; plot( a(floor(x)) , x = 1..10, thickness = 2);

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmKiYiIiMiIiIlImtHIiIiIiIiIiIkISIiNiI2IjYiNiwhIiIiIiIiIiQiIiYiIigiIioiIzYiIzgiIzoiIzw=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NiI=

Na verdade, se pudermos plotar a seq\303\274\303\252ncia juntamente com a linha correspondente: plot( [a(floor(x)),a(x)] , x = 1..10, thickness = 2, linestyle = [1,2]);

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NiI=

a := k -> 5*k + 10; a(k) $ k = 1..10; plot( {a(floor(x)),0} , x = 1..10, thickness = 2);

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmKiYiIiYiIiIlImtHIiIiIiIiIiM1IiIiNiI2IjYiNiwiIzoiIz8iI0QiI0kiI04iI1MiI1giI10iI2IiI2c=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Ig==

a := k -> 7 - 3*k; a(k) $ k = 1..10; plot( {a(floor(x)),0} , x = 1..10, thickness = 2);

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwmIiIoIiIiKiYiIiQiIiIlImtHIiIiISIiNiI2IjYiNiwiIiUiIiIhIiMhIiYhIikhIzYhIzkhIzwhIz8hI0I=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

Progress\303\265es geom\303\251tricas t\303\252m alguma similaridade com fun\303\247\303\265es exponenciais. a := k -> 10*(1/2)^(k); a(k) $ k = 1..10; plot( a(floor(x)) , x = 0..10, thickness = 2);

NiM+JSJhR2YqNiMlImtHNiI2JCUpb3BlcmF0b3JHJSZhcnJvd0c2IiwkKiYiIzUiIiIpIyIiIiIiIyUia0ciIiIiIiI2IjYiNiI=NiwiIiYjRiMiIiMjRiMiIiUjRiMiIikjRiMiIzsjRiMiI0sjRiMiI2sjRiMiJEciI0YjIiRjIyNGIyIkNyY=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

plot([a(floor(x)),a(x)] , x = 0..10, thickness = 2, linestyle =[1,2]);

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

Quando |r| < 1 ent\303\243o \303\251 decrescente como vemos acima. Quando r > 1, o gr\303\241fico \303\251 crescente. a := k -> 2*(3/2)^k; a(k) $ k = 1..10; plot([a(floor(x)),a(x)] , x = 0..10, thickness = 2, linestyle =[1,2]);

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Os gr\303\241ficos podem nos ajudar a comparar duas Sequ\303\252ncias diferentes. Por exemplo, veja essas duas: a := k -> 100*(1/3)^k; b := k -> 50*(1/2)^k;

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Observando o gr\303\241fico, podemos ver que enquanto a(k) (a reta azul) come\303\247a maior, decresce mais r\303\241pido e se torna menor do que b (a reta verde) plot( [a(floor(x)),b(floor(x)),a(x),b(x)] , x = 0..7, thickness = 2, linestyle = [1,1,2,2], color = [blue, green,yellow, orange] );

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Podemos tamb\303\251m estudar outras Sequ\303\252ncias. a := k -> (-1)^k; a(k) $ k = 1..20; plot( a(floor(x)) , x = 1..20, thickness = 2);

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a := k -> 1/k; a(k) $ k = 1..20; plot( {a(floor(x)),0} , x = 1..10, thickness = 2);

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")$"166666666!#;7$$".DJTzCi*!#7$"166666666!#;7$$"+lTY8(*!"*$"166666666!#;7$$".vo"*[W!)*!#7$"166666666!#;7$$"1\il(oOL&)*!#:$"166666666!#;7$$"/vVeWA-**!#8$"166666666!#;7$$"1E"GQMom#**!#:$"166666666!#;7$$"0v=#HA6^**!#9$"166666666!#;7$$"1jS"><ML'**!#:$"166666666!#;7$$"1v$4Y6cb(**!#:$"166666666!#;7$$"1Kq&f3n;)**!#:$"166666666!#;7$$"1)o/t0yx)**!#:$"166666666!#;7$$"1WBlG!*)Q***!#:$"166666666!#;7$$"$+"!""$"""!""-%&COLORG6&%$RGBG$""!!""$"#5!""$""!!""-%%VIEWG6$;$"#5!""$"$+"!""%(DEFAULTG-&%&_AXISG6#"""6'-%+_GRIDLINESG6'-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%)_VISIBLEG6#""!-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-&%&_AXISG6#""#6'-%+_GRIDLINESG6'-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%)_VISIBLEG6#""!-%&COLORG6&%$RGBG$""!!""$""!!""$""!!""-%*LINESTYLEG6#""!-%*THICKNESSG6#""!-%-TRANSPARENCYG6#$""!!""-%+AXESLABELSG6$Q"x6"Q!6"-%*THICKNESSG6#""#-%)_VISIBLEG6#"""-%%ROOTG6'-%)BOUNDS_XG6#$"$+%!""-%)BOUNDS_YG6#$"$I"!""-%-BOUNDS_WIDTHG6#$"%?K!""-%.BOUNDS_HEIGHTG6#$"%qJ!""-%)CHILDRENG6"-%+ANNOTATIONG6'-%)BOUNDS_XG6#$""!!""-%)BOUNDS_YG6#$""!!""-%-BOUNDS_WIDTHG6#$"%+S!""-%.BOUNDS_HEIGHTG6#$"%+S!""-%)CHILDRENG6"G6"

a := k -> -((-1)^k)/k; a(k) $ k = 1..20; plot( {a(floor(x)),0} , x = 1..10, thickness = 2);

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a := k -> k^((-1)^(k+1)) ; a(k) $ k = 1..20; plot( {a(floor(x)),0} , x = 1..10, thickness = 2);

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

a := k -> 1/ ( k + 3 + ((-1)^(k+1))*2 ); a(k) $ k = 1..15; plot( {a(floor(x)),0} , x = 1..15, thickness = 2);

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