Problem 1110 (difficulty: 3/10)

Determine whether the following series are convergent or divergent.

\(\displaystyle \sum e^{-n^2} \qquad \sum\frac{n^{10}}{3^n-2^n} \qquad \sum\frac1{\sqrt{n(n+1)}} \qquad \sum n^2 e^{-\sqrt{n}} \qquad \sum \left(n^{1/n^2}-1\right) \qquad \sum \frac{\root{n}\of{n}-1}{\log^2n} \)

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