What is the sum from k=1 to infinity of 6/k-6/(k+1) ?

The sum from k=1 to infinity of 6/k-6/(k+1) is 6

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from k=1 to infinity of 6/k-6/(k+1)

k = 1 \sum \infty \frac{6}{k} - \frac{6}{k + 1}

6

Solution steps

k = 1 \sum \infty \frac{6}{k} - \frac{6}{k + 1}

Apply Telescoping Series Test:

6

= 6

n = 0 \sum \infty 5 (\frac{3}{π})^{n}

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

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

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

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

What is the sum from k=1 to infinity of 6/k-6/(k+1) ?
The sum from k=1 to infinity of 6/k-6/(k+1) is 6