Comandos Úteis e Simples
Seção 2.4: Adição de termos vs. o cálculo da diferença finita
| > | restart; |
| > | a := add( 1/k, k=1..10 ); |
| > | k; |
| > | s := sum( 1/k, k=1..10 ); |
| > | k; |
| > | S := Sum( 1/k, k=1..10 ); |
| > | evalf( S ); |
| > | add( 1/k, k=1..n ); |
Error, unable to execute add
| > | S[n] := sum( 1/k, k=1..n ); |
![S[n] := Psi(n+1)+gamma](images/247.gif){kind=small}
| > | limit( S[n] - log(n), n=infinity ); |
| > | asympt( S[n], n ); |
| > | restart; |
| > | c := proc( n ) option remember; -1/(n-1)*add( binomial(n-i+1, i+1)*c(n-i), i=1..n-1 ) end proc; |
| > | c(1) := 1; |
| > | seq(c(k),k=1..8); |
| > | Bseries := v -> `if`(v=0,1.,evalf(Sum('c(n)*v^(n-1)', n=1..infinity))); |
| > | Bseries(0); |
| > | Bseries(0.001); |
| > | Bseries(0.05); |
| > |
| > | restart; |
| > | currentdir("C:/books/ess/programs"); |
| > | read "cesaro.mpl"; |
| > | CesaroSum( (-1)^n, n ); |
| > | normal( CesaroSum( cos(n*x), n ) ); |
| > | part := sum( cos(n*x), n=0..60 ); |
| > | plot( part, x=0..2*Pi, y=-1..2, style=POINT, numpoints=1001, symbol=POINT, symbolsize=20, colour=black ); |
![[Maple Plot]](images/2424.gif)
| > | CesaroSum( sin(n*x), n, 1 ); |
| > | CesaroSum( x^n/n^2,n, 1 ); |
![limit((m*x*hypergeom([1, 1, 1],[2, 2],x)+sum(-x^k*x/(k+1)^2*hypergeom([1, k+1, k+1],[2+k, 2+k],x),k = 1 .. m))/m,m = infinity)](images/2426.gif)
| > | sum( 1/sqrt(n), n=1..k ); |
| > | sum( x^n/n^2, n=1..infinity ); |
| > | restart; |
| > | alias(alpha=RootOf(z^6+z+1, z)); |
| > | Sum(1/k, k=alpha); |
| > | value( % ); |
| > | Product(1/(k+1), k=alpha); |
| > | value( % ); |
| > | product(1/(1+k^2), k=1..n ); |
| > |
| > |
| > |
| > |