What is the sum from k=1 to infinity of 1/(k^6) ?

The sum from k=1 to infinity of 1/(k^6) is converges

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 1/(k^6)

k = 1 \sum \infty \frac{1}{k ^{6}}

converges

Solution steps

k = 1 \sum \infty \frac{1}{k ^{6}}

Apply p-Series Test:

converges

= converges

k = 0 \sum \infty (0.8)^{k}

n = 1 \sum \infty \frac{5}{1 + n ^{2}}

x = 0 \sum \infty \frac{1}{1 - x}

n = 1 \sum \infty 4^{n - 1}

n = 1 \sum \infty 2 (0.1)^{n - 1}

What is the sum from k=1 to infinity of 1/(k^6) ?
The sum from k=1 to infinity of 1/(k^6) is converges