What is the sum from k=1 to infinity of ke^{-6k^2} ?

The sum from k=1 to infinity of ke^{-6k^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 ke^{-6k^2}

k = 1 \sum \infty k e^{- 6 k^{2}}

converges

Solution steps

k = 1 \sum \infty k e^{- 6 k^{2}}

Apply Series Ratio Test:

converges

= converges

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

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

n = 0 \sum \infty \frac{1}{1 - n ^{2}}

n = 0 \sum \infty \frac{n}{1 + n}

x = 0 \sum \infty \frac{x ^{x}}{x !}

What is the sum from k=1 to infinity of ke^{-6k^2} ?
The sum from k=1 to infinity of ke^{-6k^2} is converges