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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty \frac{n ^{3}}{n + 1}

n = 2 \sum \infty \frac{7}{5 ^{n}}

n = 1 \sum \infty \frac{1}{2 + 3 n}

n = 1 \sum \infty \frac{1}{7 ^{n} + 7}

n = 1 \sum \infty \frac{9}{10}

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