# Power series writing terms

Can someone explain how I should be solving for theses terms? I got my series to be $10(-7x)^n$, but I dont know what to do from there.

Represent the function $f(x)=\frac{10}{(1-7x)}$ as a power series $$f(x)=\sum_{n=0}^\infty c_nx^n$$

Find the following coefficients:

$c_0=\color{green}{10(-7(2))^0}\\c_1=\\c_2=\\c_3=\\c_4=$

$R=$
• Where does that "2" come from, in $10(-7(2))^0$? – Gerry Myerson Apr 22 '15 at 12:37
• Use the binomial series for $g(y)=(1-y)^{-1}$ with $y=7x$ and them multiply through by $10$. The radius of convergence is then inherited from that of the series for $g(y)$ – Conrad Turner Apr 22 '15 at 13:10
I think that in the preamble of your question you should have $10(7x)^n$ instead of the negative (this from Geometric series). It should be clear then that $c_n=10\cdot 7^n$. As far as the radius of convergence you should know that in the Geometric series, $|7x|<1$.