What is the sum from k=0 to infinity of (3/4)^k ?

The sum from k=0 to infinity of (3/4)^k is 4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from k=0 to infinity of (3/4)^k

k = 0 \sum \infty (\frac{3}{4})^{k}

4

Solution steps

k = 0 \sum \infty (\frac{3}{4})^{k}

Apply Series Geometric Test:

4

= 4

n = 1 \sum \infty (1 - \frac{2}{n})^{3 n}

n = 6 \sum \infty \frac{2}{n - 5}

n = 0 \sum \infty \frac{1}{e ^{- n}}

n = 0 \sum \infty \frac{1}{1 + 3 n ^{3}}

n = 1 \sum \infty (\frac{5}{7})^{n}

What is the sum from k=0 to infinity of (3/4)^k ?
The sum from k=0 to infinity of (3/4)^k is 4