Find the Taylor series for the function f(x) = 1/((1-x)^2) valid for x near zero, using the fact that 1/(1-x) = the sum from k=0 to infinity of x^k.

I'm stuck. Please help me! Thanks.

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- Apr 27th 2010, 05:09 PMMathboCalculus: Taylor Series
Find the Taylor series for the function f(x) = 1/((1-x)^2) valid for x near zero, using the fact that 1/(1-x) = the sum from k=0 to infinity of x^k.

I'm stuck. Please help me! Thanks. - Apr 27th 2010, 05:26 PMDeadstar
Differentiate $\displaystyle \frac{1}{1-x}$ and see what you get...

Apply the same to the sum you're given - Apr 27th 2010, 06:19 PMMathbo
When I took the derivative, I got my function and when I took the derivative of the sum, I got f(x)=sum from K=0 to infinity of (K)x^K, but it seems like sum from K=0 to infinity of (1+K)x^K better describes my function. Is that the answer? Is it considered a Taylor Series when you don't write out all the terms, but write it as an infinite sum instead?

- Apr 28th 2010, 02:23 AMDeadstar