What is the sum from n=1 to infinity of n^{-3} ?

The sum from n=1 to infinity of n^{-3} is converges

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sum from n=1 to infinity of n^{-3}

n = 1 \sum \infty n^{- 3}

converges

Solution steps

n = 1 \sum \infty n^{- 3}

Apply exponent rule:

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

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

Apply p-Series Test:

converges

= converges

What is the sum from n=1 to infinity of n^{-3} ?
The sum from n=1 to infinity of n^{-3} is converges