What is the sum from k=1 to infinity of ke^{-16k} ?

The sum from k=1 to infinity of ke^{-16k} 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^{-16k}

k = 1 \sum \infty k e^{- 16 k}

converges

Solution steps

k = 1 \sum \infty k e^{- 16 k}

Apply Series Ratio Test:

converges

= converges

k = 1 \sum \infty k e^{- 15 k}

n = 1 \sum \infty \frac{1 ^{n}}{n ^{3}}

n = 1 \sum \infty \frac{5}{n} - \frac{5}{n ^{2}}

n = 0 \sum \infty n - 1

n = 1 \sum \infty (1.075)^{n}

What is the sum from k=1 to infinity of ke^{-16k} ?
The sum from k=1 to infinity of ke^{-16k} is converges