What is the sum from n=0 to infinity of 1/(2^nn) ?

The sum from n=0 to infinity of 1/(2^nn) is converges

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 1/(2^nn)

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

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

n = 1 \sum \infty ln (\frac{n + 3}{n})

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

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

j = 1 \sum \infty 5^{- 3 j}

What is the sum from n=0 to infinity of 1/(2^nn) ?
The sum from n=0 to infinity of 1/(2^nn) is converges