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

The sum from n=1 to infinity of 2/(n^2) is converges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

sum from n=1 to infinity of 2/(n^2)

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

converges

Solution steps

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

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Apply p-Series Test:

converges

= 2 converges

= converges

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