For what values of $x$ does the geometric series $(2+x)+(2+x)^2+(2+x)^3+\cdots$ converge? I am stuck on this geometric series question:
For what values of $x$ would the infinite geometric series $(2+x)+(2+x)^2+(2+x)^3+\cdots$ converge?
Formula for series:
$$S_n=\frac{a(1-r^n)}{1-r}$$
The first term $a=(2+x)$ and the common ratio $r=(2+x)$ ?
$$S_n=\frac{(2+x)(1-(x+2)^n)}{1-(x+2)}$$
Am I totally wrong on this or somewhat on the right track?
Thanks

Yuo're right as far as you've taken it.  Now you need to recall the series converges if $-1<r<1$ and diverges otherwise.
