What is the sum from n=0 to infinity of 1/n-1/(n+1) ?

The sum from n=0 to infinity of 1/n-1/(n+1) is 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sum from n=0 to infinity of 1/n-1/(n+1)

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

1

Solution steps

n = 1 \sum \infty \frac{1}{n} - \frac{1}{n + 1}

Apply Telescoping Series Test:

1

= 1

x \to - 5 - lim (\frac{x + 2}{x + 5})

\frac{3}{s + 4}

\int (5 x^{3} - 18)^{7} 15 x^{2} d x

\int \frac{4 e ^{x}}{e ^{2 x} + 10 e ^{x} + 25} d x

\frac{d y}{d x} + x^{2} y = 2 x^{2}

What is the sum from n=0 to infinity of 1/n-1/(n+1) ?
The sum from n=0 to infinity of 1/n-1/(n+1) is 1