What is the sum from n=0 to infinity of pi^{-n} ?

The sum from n=0 to infinity of pi^{-n} is pi/(pi-1)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

sum from n=0 to infinity of pi^{-n}

n = 0 \sum \infty π^{- n}

\frac{π}{π - 1}

Decimal

1.46694 \dots

Solution steps

n = 0 \sum \infty π^{- n}

Simplify

π^{- n} : \frac{1}{π ^{n}}

= n = 0 \sum \infty \frac{1}{π ^{n}}

Apply Series Geometric Test:

\frac{π}{π - 1}

= \frac{π}{π - 1}

What is the sum from n=0 to infinity of pi^{-n} ?
The sum from n=0 to infinity of pi^{-n} is pi/(pi-1)