What is the sum from n=0 to infinity of 1/(2n^3) ?

The sum from n=0 to infinity of 1/(2n^3) is converges

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/(2n^3)

n = 0 \sum \infty \frac{1}{2 n ^{3}}

converges

Solution steps

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

Apply the constant multiplication rule:

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

= \frac{1}{2} \cdot n = 1 \sum \infty \frac{1}{n ^{3}}

Apply p-Series Test:

converges

= \frac{1}{2} converges

= converges

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

n = 0 \sum \infty \frac{n + 1}{3 n + 1}

n = 0 \sum \infty e^{- 14 n}

n = 1 \sum \infty \frac{n}{2 n ^{2} + 11}

n = 1 \sum \infty \frac{6}{9 n + 1}

What is the sum from n=0 to infinity of 1/(2n^3) ?
The sum from n=0 to infinity of 1/(2n^3) is converges