What is the sum from k=1 to infinity of k^3e^{-k^2} ?

The sum from k=1 to infinity of k^3e^{-k^2} is converges

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sum from k=1 to infinity of k^3e^{-k^2}

k = 1 \sum \infty k^{3} e^{- k^{2}}

converges

Solution steps

k = 1 \sum \infty k^{3} e^{- k^{2}}

Apply Series Ratio Test:

converges

= converges

(x^{2} + y) d x + (x - e^{y}) d y = 0

y = 4

\frac{d}{d x} (\frac{1}{x ^{- 2}})

\frac{\partial}{\partial x} (\frac{e \cdot x}{c - x})

x \to 4 - lim (\frac{- 2}{x ^{2} - 16})

What is the sum from k=1 to infinity of k^3e^{-k^2} ?
The sum from k=1 to infinity of k^3e^{-k^2} is converges