What is the sum from k=1 to infinity of 1/(k^2+k) ?

The sum from k=1 to infinity of 1/(k^2+k) is 1

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 1/(k^2+k)

k = 1 \sum \infty \frac{1}{k ^{2} + k}

1

Solution steps

k = 1 \sum \infty \frac{1}{k ^{2} + k}

Apply Telescoping Series Test:

1

= 1

n = 0 \sum \infty \frac{cos ( nπ )}{5}

n = 2 \sum \infty 7 e^{- 3 n}

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

n = 0 \sum \infty \frac{n}{n}

k = 2 \sum \infty (- 0.8)^{k}

What is the sum from k=1 to infinity of 1/(k^2+k) ?
The sum from k=1 to infinity of 1/(k^2+k) is 1