What is the sum from n=1 to infinity of ne^{-n^2} ?

The sum from n=1 to infinity of ne^{-n^2} is converges

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sum from n=1 to infinity of ne^{-n^2}

n = 1 \sum \infty n e^{- n^{2}}

converges

Solution steps

n = 1 \sum \infty n e^{- n^{2}}

Apply Series Ratio Test:

converges

= converges

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What is the sum from n=1 to infinity of ne^{-n^2} ?
The sum from n=1 to infinity of ne^{-n^2} is converges