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I really don't know which trick should I use to solve convergence of this sum:

[tex]

\sum_{n=1}^{\infty} a_{n}

[/tex]

where

[tex]

a_{n} = \left( 1 - \frac{1}{n^2} \right)^{n} - 1

[/tex]

Neither binomial development nor writing first few terms helped me, and because all terms of this sum are negative, I can't use many of theorems...

It seems it could have something to do withe, but I can't see the adjustment to get it exactly...

Thank you for any suggestion.

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# Another tricky sum

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