Power Series

[thebigace]

Hi,
So I am doing a problem with power series, and it says the function f(x) = 1/((1-7x)^2) is represented as a power series f(x) = sum n=0^infinity of c(n)x^n
Then it wants me to find the first few coefficients in the power series. I know the first one is 1, and the radius of convergence is 1/7. and I tried to get the equation in the for 1/(1-u) so that I could use a geometric series 1+u+u^2... but my u=14x+49x^2 and it isn't working out like I thought. Any help would be appreciated

 

[pka]

When you say that “it is not working out”, what do you mean?
It seems correct to me:
\(\displaystyle \begin{array}{l}
\sum\limits_{k = 0}^\infty {x^k } = \frac{1}{{1 - x}} \\
\sum\limits_{k = 0}^\infty {x^{k + 1} } = \frac{x}{{1 - x}} \\
\sum\limits_{k = 0}^\infty {\left( {k + 1} \right)x^k } = \frac{1}{{\left( {1 - x} \right)^2 }} \\
\sum\limits_{k = 0}^\infty {7^k \left( {k + 1} \right)x^k } = \frac{1}{{\left( {1 - 7x} \right)^2 }} \\
\end{array}\)