What is the sum from n=0 to infinity of n^2e^n ?

The sum from n=0 to infinity of n^2e^n is diverges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from n=0 to infinity of n^2e^n

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

diverges

Solution steps

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

Apply Series Ratio Test:

diverges

= diverges

n = 0 \sum \infty \frac{n ^{3}}{2 - n}

n = 1 \sum \infty \frac{2}{3 n + 3}

n = 1 \sum \infty \frac{6}{n} - \frac{6}{n ^{2}}

n = 1 \sum \infty 30 (0.1)^{n}

n = 1 \sum \infty \frac{8}{n} + 3^{- n}

What is the sum from n=0 to infinity of n^2e^n ?
The sum from n=0 to infinity of n^2e^n is diverges