Does the series converge or diverge? If it converges find the sum.
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$\displaystyle \sum_{n=1}^{\infty} {ne^{-n^2}}$ use the integral test to show convergence ... have to think about the actual sum.
Even better, $\displaystyle \sqrt[n]{{ne^{ - n^2 } }} = \frac{{\sqrt[n]{n}}} {{e^n }}$
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