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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

x \to 4 lim (5 x^{2} - 2 x)

\frac{4 + t}{t e ^{t}}

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

\int_{0}^{1} x 1 + 8 x^{2} d x

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

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