Infinite Geometric Series I'm currently stuck on this question:
What is the value of c if $\sum_{n=1}^\infty (1 + c)^{-n}$ = 4 and c > 0?
This appears to be an infinite geometric series with a = 1 and r = $(1 + c)^{-1}$, so if I plug this all into the sum of infinite geometric series formula $S = \frac{a}{1 - r}$, then I get the following:
$4 = \frac{1}{1 - (1 + c)^{-1}}$, which eventually lets me solve c = $\frac{1}{3}$. But this answer isn't right. Can someone help me out? Thanks in advance!

First of all, to converge it must be that 
$$\;\frac1{|c+1|}<1\iff |c+1|>1 \iff c>0\;\;or\;\;c<-2\;$$  
and applying the well known formula for the sum of a converging gometric sieres we get
$$4=\sum_{n=1}^\infty\frac1{(c+1)^n}=\frac{\frac1{c+1}}{1-\frac1{c+1}}$$
you get the value of $\;c\;$ ...(the first summand is not $\;1\;$ ...)
