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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\int \frac{3 x ^{2}}{1 - x ^{2}} d x

\int \frac{1}{p - z} + \frac{1}{z} d z

\int 4 (x - 1) d x

\frac{x ^{6}}{2 - x ^{5}}

f (x) = \frac{5}{4} x^{\frac{4}{3}}

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