What is the sum from n=0 to infinity of (2n)/(1+n^4) ?

The sum from n=0 to infinity of (2n)/(1+n^4) is converges

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

sum from n=0 to infinity of (2n)/(1+n^4)

n = 0 \sum \infty \frac{2 n}{1 + n ^{4}}

converges

Solution steps

n = 0 \sum \infty \frac{2 n}{1 + n ^{4}}

Apply the constant multiplication rule:

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

= 2 \cdot n = 0 \sum \infty \frac{n}{1 + n ^{4}}

Apply Series Comparison Test:

converges

= 2 converges

= converges

What is the sum from n=0 to infinity of (2n)/(1+n^4) ?
The sum from n=0 to infinity of (2n)/(1+n^4) is converges