What is the sum from n=0 to infinity of 2^{-2n} ?

The sum from n=0 to infinity of 2^{-2n} is 4/3

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 2^{-2n}

n = 0 \sum \infty 2^{- 2 n}

\frac{4}{3}

Decimal

1.33333 \dots

Solution steps

n = 0 \sum \infty 2^{- 2 n}

Simplify

2^{- 2 n} : \frac{1}{2 ^{2 n}}

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

2^{2 n} = 4^{n}

= n = 0 \sum \infty \frac{1}{4 ^{n}}

Apply Series Geometric Test:

\frac{4}{3}

= \frac{4}{3}

What is the sum from n=0 to infinity of 2^{-2n} ?
The sum from n=0 to infinity of 2^{-2n} is 4/3