What is the sum from n=0 to infinity of ne^{-2n^2} ?

The sum from n=0 to infinity of ne^{-2n^2} is converges

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sum from n=0 to infinity of ne^{-2n^2}

n = 0 \sum \infty n e^{- 2 n^{2}}

converges

Solution steps

n = 0 \sum \infty n e^{- 2 n^{2}}

Apply Series Ratio Test:

converges

= converges

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

n = 0 \sum \infty 9 (\frac{8}{9})^{n}

n = 10 \sum \infty \frac{1}{n ln ( n )}

n = 1 \sum \infty 0. 1^{n}

i = 1 \sum \infty \frac{1}{i ( i + 1 )}

What is the sum from n=0 to infinity of ne^{-2n^2} ?
The sum from n=0 to infinity of ne^{-2n^2} is converges