What is the sum from n=0 to infinity of ne^{-n^2} ?

The sum from n=0 to infinity of ne^{-n^2} is converges

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sum from n=0 to infinity of ne^{-n^2}

n = 0 \sum \infty n e^{- n^{2}}

converges

Solution steps

n = 0 \sum \infty n e^{- n^{2}}

Apply Series Ratio Test:

converges

= converges

f (x) = (1 + 3 x^{2}) (x - x^{2})

y^{^{'}} + 2 y = t e^{- 2 t}, y (1) = 0

\int [(3 - x^{2})^{3}] d x

\int \frac{- 3}{( x - 2 ) ( x ^{2} + 4 )} d x

x \to 2 + lim (2)

What is the sum from n=0 to infinity of ne^{-n^2} ?
The sum from n=0 to infinity of ne^{-n^2} is converges