Find the values of $x$ for which the series converges.
$$\sum _{ n=1 }^{ \infty }{ (x+5)^{ n } } $$
Find the sum of the series for those values of $x$.
What I did:
I know that I have to have the absolute value of my common ratio, $(x+5)$, be less than $1$, so I set up the following inequality:
$$-1<(x+5)<1$$
By solving it we get:
$$-6<x<-4$$
Now, I am wondering how I can use those values of $x$ to find the sum of the series. I am at a complete loss here, so I would appreciate any hint that will help me solve this on my own.