What is the sum from k=1 to infinity of 9/k-9/(k+1) ?

The sum from k=1 to infinity of 9/k-9/(k+1) is 9

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 9/k-9/(k+1)

k = 1 \sum \infty \frac{9}{k} - \frac{9}{k + 1}

9

Solution steps

k = 1 \sum \infty \frac{9}{k} - \frac{9}{k + 1}

Apply Telescoping Series Test:

9

= 9

n = 1 \sum \infty \frac{1}{4 + n ^{2}}

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

n = 0 \sum \infty \frac{1}{1 - 6 n}

n = 0 \sum \infty (0.2)^{n}

n = 0 \sum \infty \frac{n ^{2}}{9 ^{n}}

What is the sum from k=1 to infinity of 9/k-9/(k+1) ?
The sum from k=1 to infinity of 9/k-9/(k+1) is 9