Differentiating a power series

[Poetria]

Homework Statement

[/B]
Differentiate the power series for $\frac 1 {1-x}$ to find the power series for $\frac 1 {(1-x)^2}$
(Note the summation index starts at n = 1)

2. The attempt at a solution


$\sum_{n=1}^\infty n*x^{n-1}$

 

[BvU]

What is the power series for 1/(1-x) ?

 

[Poetria]

What is the power series for 1/(1-x) ?

$\sum_{n=0}^\infty x^n$

OK?

Series expansion at x = 0
1+x+x^2+x^3...

So if I differentiate:

0+1+2*x+3x^3...

 

[BvU]

Good. Perfect, in fact. If you want you can rewrite it in a more conventional form ($\ \ \displaystyle\sum_{n=0}^\infty \ \$)

 

[Poetria]

Good. Perfect, in fact. If you want you can rewrite it in a more conventional form ($\ \ \displaystyle\sum_{n=0}^\infty \ \$)

Ok. :) Many thanks. :)

$\sum_{n=0}^\infty (n+1)*x^n$