# Exact value of a series question

The value of the series $$\sum_{n=1}^\infty \frac{1}{n^2}$$ is well-known to be $\pi^2/6$ and there are many proofs of this http://en.wikipedia.org/wiki/Basel_problem. How can one show that the seemingly related series $$\sum_{n=3}^\infty \frac{1}{n^2 - 4}$$ has sum $25/48$?

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Hint: $\dfrac{1}{n-2}-\dfrac{1}{n+2} = \dfrac{4}{n^2-4}$