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

The sum from x=1 to infinity of xe^{-x^2} is converges

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sum from x=1 to infinity of xe^{-x^2}

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

n = 3 \sum \infty \frac{n}{5 ^{n}}

k = 1 \sum \infty k^{\frac{1}{k}}

n = 1 \sum \infty \frac{1}{n ^{3} + 5}

n = 1 \sum \infty \frac{1}{n ^{3} - 5 n ^{2}}

k = 1 \sum \infty \frac{k ^{2}}{4 ^{k}}

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