What is the sum from n=0 to infinity of 1/(n^{1/6)} ?

The sum from n=0 to infinity of 1/(n^{1/6)} is diverges

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^{1/6)}

n = 0 \sum \infty \frac{1}{n ^{\frac{1}{6}}}

diverges

Solution steps

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

Apply p-Series Test:

diverges

= diverges

n = 0 \sum \infty 5 (- \frac{1}{2})^{n}

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

n = 0 \sum \infty \frac{1}{7 n + 1}

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

n = 0 \sum \infty \frac{1}{n 6 ^{n}}

What is the sum from n=0 to infinity of 1/(n^{1/6)} ?
The sum from n=0 to infinity of 1/(n^{1/6)} is diverges