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

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

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

\frac{d}{d x} (\frac{1}{y} e^{x y} - ln (y^{2}))

\frac{d}{d x} (7 x^{\frac{1}{2}} + x^{\frac{3}{2}})

n = 1 \sum \infty arctan (2 n)

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

\int \frac{5}{x ^{2} + 16} d x

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