Leibniz Alternating Series Test Can someone help me find a Leibniz Series (alternating sum) that converges to $5$ ? 
Does such a series even exist?
Thanks in advance!!!
I've tried looking at a series of the form $ \sum _ 1 ^\infty (-1)^{n} q^n $ which is a geometric series ... But I get $q>1 $ , which is impossible... Does someone have an idea? 

You can cook up an alternating series that hits any sum $S$ you like as follows.


*

*Pick a geometric series (with first term of 1) with geometric ratio $r$, with $-1<r<0$. Its sum will be ${1\over 1-r}$.

*This is also an alternating series since $\sum_{n=0}^\infty r^n=\sum_{n=0}^\infty(-1)^{n}|r|^n$.

*If you want the final sum to be $S$, then you just need to multiply the original geometric series by a constant $k$ so that $k\sum_{n=0}^\infty r^n=S$, but this implies $k=S(1+|r|)$.

*Thus, you use $$S(1+|r|)\sum_{n=0}^\infty r^n=S(1+|r|)\sum_{n=0}^\infty (-1)^{n}|r|^n, \quad -1<r<0.$$ It will be alternating and have sum $S$.
