What is the sum from n=1 to infinity}n^{-sqrt(2 of) ?

The sum from n=1 to infinity}n^{-sqrt(2 of) 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=1 to infinity}n^{-sqrt(2 of)

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

converges

Solution steps

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

Apply exponent rule:

a^{- b} = \frac{1}{a ^{b}}

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

Apply p-Series Test:

converges

= converges

n = 2 \sum \infty \frac{3}{5 ^{n - 1}}

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

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

n = 1 \sum \infty cos (\frac{17}{n})

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

What is the sum from n=1 to infinity}n^{-sqrt(2 of) ?
The sum from n=1 to infinity}n^{-sqrt(2 of) is converges