Sum of the Reciprocal of the Difference of Two Squares

Is there a closed-form expression for the sum:

$$\sum \limits_{i=2}^{n} \frac{1}{i^2-1}$$

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What is a closed-form expression? +1 by the way. –  Sachin Kainth Oct 10 '12 at 23:22

Hint $$\frac{1}{i^2-1}=\frac{1}{2}\left(\frac{1}{i-1}-\frac{1}{i+1}\right)$$ Now use telescopy.
$$-\frac{1}{2}\,{\frac {1+2\,n}{ \left( n+1 \right) n}} + \frac{3}{4} \,.$$