What is the sum from k=1 to infinity of ke^{-4k^2} ?

The sum from k=1 to infinity of ke^{-4k^2} is converges

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sum from k=1 to infinity of ke^{-4k^2}

k = 1 \sum \infty k e^{- 4 k^{2}}

converges

Solution steps

k = 1 \sum \infty k e^{- 4 k^{2}}

Apply Series Ratio Test:

converges

= converges

n = 2 \sum \infty \frac{7}{n ln ( n )}

n = 0 \sum \infty \frac{n !}{40 0 ^{n}}

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

n = 1 \sum \infty cos (\frac{6}{n})

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

What is the sum from k=1 to infinity of ke^{-4k^2} ?
The sum from k=1 to infinity of ke^{-4k^2} is converges