# Power series calculus 2?

• April 15th 2010, 08:54 PM
andrewt328
Power series calculus 2?
given that a power series for 1/(1-x) is sum.n=0,inf. x^n

what is the power series for 1/(1-x)^2

thanks
• April 15th 2010, 09:00 PM
Failure
Quote:

Originally Posted by andrewt328
given that a power series for 1/(1-x) is sum.n=0,inf. x^n

what is the power series for 1/(1-x)^2

thanks

For example, by use of the "derivation trick", you get
$\frac{1}{(1-x)^2}=\frac{d}{dx}\frac{1}{1-x}=\frac{d}{dx}\sum_{n=0}^\infty x^n=\sum_{n=0}^\infty\frac{d}{dx}x^n=\sum_{n=1}^\i nfty n x^{n-1}=\sum_{n=0}^\infty (n+1)x^n$
• April 15th 2010, 09:07 PM
andrewt328
thank you!