Find the first 5 coefficients of the series $\frac{6x}{x+9} = \sum_{n=0}^\infty C_n x^n$ I rewrote the equation series as $$ \frac69 \sum_{n=0}^\infty \left(\frac{-1}{9}\right)^n  x^{n+1} $$
And therefore have coefficients of $C_0 = 6/9, C_1 = \left( 6/9 \right) \left(\frac{-1}{9}\right)^1, C_2 = ( 6/9 )\left(\frac{-1}{9}\right)^2, C_3 = \cdots $ This is wrong however and I'm not sure why. If anyone knows the solution to this could they point me in the right direction?

$\frac{6x}{x+9}=6-\frac{54}{9+x}=6-\frac{6}{1-\frac{-x}{9}}=6-6\sum_{n=0}^{\infty}(-\frac{x}{9})^n \quad \forall x,\mid{x}\mid<9$.
Now let $n=0,1,2,4$ and calculate $c_{n}$s.
