Need to find a value to satisfy a given geometric series equation but it seems there is no solution, is there one?

Question

The geometric series given is this:

$$\sum_\limits{n=1}^\infty \frac{1}{(1+c)^n} = -2$$

I must find c to make the equation true. I used $a\over (1-r)$, substituting:

${(1+c)^{-1} \over 1 - (1+c)^{-1}} = -2$ and arrive at $c= -1/2$. This value however makes the series diverge as $r$ is not between $-1$ and $1$.

Please be so kind as to verify that there is no solution, or point me in the right direction or give the solution. Thank you very much!

Answer 1

The series cannot converge to $-2$ so $c$ has no solution.