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

The sum from k=1 to infinity of ke^{-2k^2} is converges

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sum from k=1 to infinity of ke^{-2k^2}

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 1 \sum \infty (\frac{7}{9})^{n - 1}

n = 3 \sum \infty \frac{4 ^{n}}{3 ^{n}}

n = 1 \sum \infty sec (n)

n = 0 \sum \infty \frac{2}{5}

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

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