What is the sum from n=1 to infinity of ne^{-7n^2} ?

The sum from n=1 to infinity of ne^{-7n^2} is converges

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sum from n=1 to infinity of ne^{-7n^2}

n = 1 \sum \infty n e^{- 7 n^{2}}

converges

Solution steps

n = 1 \sum \infty n e^{- 7 n^{2}}

Apply Series Ratio Test:

converges

= converges

k = 0 \sum \infty (0.6)^{k}

n = 1 \sum \infty \frac{n ^{2}}{7 ^{n}}

n = 0 \sum \infty \frac{4}{2 n + 3}

n = 0 \sum \infty 9^{- n}

n = 2 \sum \infty \frac{1}{n ln ( n ^{3} )}

What is the sum from n=1 to infinity of ne^{-7n^2} ?
The sum from n=1 to infinity of ne^{-7n^2} is converges