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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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

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

n = 0 \sum \infty n^{- s i n (1)}

n = 1 \sum \infty \frac{2 n}{7 n - 3}

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

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