Thread: Represent the function as a power series, another one

1. Represent the function as a power series, another one

I have another function $\displaystyle \frac{1}{1+25x^2}$ wich I have to represent as as a power series $\displaystyle f(x) = \sum_{n=0}^{\infty} c_nx^n$

it seems to me that I got something different because the coefficients I get are not correct.

what I got is $\displaystyle f(x) = \sum_{n=0}^{\infty} (-25)^{n}x^{2n}$ with a Radius of convergence R= 1/5

the first few coefficients I get are $\displaystyle 1-25+25^{2}-25^{3}+25^{4}$

I know that my radius of convergence is correct, but I can't understand where is my mistake with the coefficients,

thank you

2. Re: Represent the function as a power series, another one

What you have is correct. You have forgotten that because there will only be even powers of x, the terms with the odd powers of x have 0 coefficient.

3. Re: Represent the function as a power series, another one

Originally Posted by Prove It
What you have is correct. You have forgotten that because there will only be even powers of x, the terms with the odd powers of x have 0 coefficient.
thanks a lot, you made me to revise the geometric series,