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

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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

y^{^{''}} + 64 y = 0, y (0) = 2, y^{^{'}} (0) = 1

(- x y sin (x) + 2 y cos (x)) d x + (2 x cos (x)) d y = 0

t^{2} e^{- 3 t} sin (4 t)

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

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