What is the sum from n=1 to infinity of ne^{-5n^2} ?

The sum from n=1 to infinity of ne^{-5n^2} is converges

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sum from n=1 to infinity of ne^{-5n^2}

n = 1 \sum \infty n e^{- 5 n^{2}}

converges

Solution steps

n = 1 \sum \infty n e^{- 5 n^{2}}

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty (0.8)^{n}

n = 1 \sum \infty (\frac{3}{7})^{n}

k = 1 \sum \infty 2^{- k}

k = 5 \sum \infty (\frac{e}{π})^{k - 1}

k = 4 \sum \infty \frac{1}{( k - 1 ) ^{4}}

What is the sum from n=1 to infinity of ne^{-5n^2} ?
The sum from n=1 to infinity of ne^{-5n^2} is converges