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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\frac{\partial}{\partial x} (4 x^{6} + x y^{3} + 2 y^{4})

\frac{\partial}{\partial y} (y ln (x^{2} y))

\frac{\partial}{\partial x} (x e^{x y} + y e^{- x})

\int 1 - sin^{2} (θ) d θ

\frac{\partial}{\partial y} (x^{2} - y^{2} + 2 x y)

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