- #1

crazycool2

- 16

- 0

\begin{equation}

\sum_{n=0}^{\infty} c_{n+2}x^n+e^{-x} \sum_{n=0}^{\infty}c_{n}x^n \\

\text{where}\\

e^{-x}=\frac{1}{\sum_{n=0}^{\infty}\frac{x^n}{n!}}\\

\sum_{n=0}^{\infty} c_{n+2}x^n+\frac{ \sum_{n=0}^{\infty}c_{n}x^n }{\sum_{n=0}^{\infty}\frac{x^n}{n!}}

\end{equation}

now my problem is I have the x

^{n}in every term and the limits are the same, but I have a fraction of sums and I want to a way to make it simpler. can the x

^{n}cancel each other in the fraction. if so

i then have

\begin{equation}

\sum_{n=0}^{\infty} c_{n+2}x^n+ \sum_{n=0}^{\infty} c_n*n!

\end{equation}

Is this even allowed?