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> Prove that the series $\sum\limits\_{n=0}^{\infty}\frac{1}{n(n+1)+x}$ for $x>0$ contains a value c such that $f(c)=2\pi$.
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It seems like this is somehow related to the fact that 
$$1-1/3+1/5-...=\pi/4$$
but I can't figure out how to manipulate the proof for that equation to align with this problem. 

I know that I can use the Mean Value Theorem to show this since when $x$ approaches $0$, the sum is 1. I just need to show that a value for $x$ exists so that $f(x)>2\pi$.