What is the sum from n=0 to infinity of 5/(pi^n) ?

The sum from n=0 to infinity of 5/(pi^n) is 5*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 5/(pi^n)

n = 0 \sum \infty \frac{5}{π ^{n}}

5 \cdot \frac{π}{π - 1}

Decimal

7.33471 \dots

Solution steps

n = 0 \sum \infty \frac{5}{π ^{n}}

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Apply Series Geometric Test:

\frac{π}{π - 1}

= 5 \cdot \frac{π}{π - 1}

What is the sum from n=0 to infinity of 5/(pi^n) ?
The sum from n=0 to infinity of 5/(pi^n) is 5*pi/(pi-1)