What is the sum from n=0 to infinity of (7/10)^n ?

The sum from n=0 to infinity of (7/10)^n is 10/3

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 (7/10)^n

n = 0 \sum \infty (\frac{7}{10})^{n}

\frac{10}{3}

Solution steps

n = 0 \sum \infty (\frac{7}{10})^{n}

Apply Series Geometric Test:

\frac{10}{3}

= \frac{10}{3}

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

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

n = 0 \sum \infty \frac{5}{1 1 ^{n}}

n = 1 \sum \infty (\frac{8 π}{9})^{n}

n = 2 \sum \infty \frac{n !}{6 ^{n}}

What is the sum from n=0 to infinity of (7/10)^n ?
The sum from n=0 to infinity of (7/10)^n is 10/3