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

The sum from n=1 to infinity of 1/(2^{n-1)} 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=1 to infinity of 1/(2^{n-1)}

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

converges

Solution steps

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

Apply Series Ratio Test:

converges

= converges

x \to \infty lim (0^{0})

x \to 3 lim (\frac{1}{( x - 3 )})

\int_{0}^{1} 2 x^{2} (x^{3} - 1)^{3} d x

\int x^{2} - 16 d x

\frac{d}{d x} (2 ln (2 x))

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