$\displaystyle a_n = \sum^{\infty}_{n=1}\frac{-1}{2(n+2)(n+3)}$

It is known that limit of the terms is $\displaystyle 0$ and that the series converges to $\displaystyle \frac{-1}{6}$.

I have a problem that asks for $\displaystyle c_n$ where $\displaystyle a_n = c_n - c_{n+1}$.

Maybe it is simple, but I'm having trouble envisioning how to find $\displaystyle c_n$. If anyone has any tips or hints, I'd greatly appreciate it.

Thanks for your consideration,

-Austin Martin