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

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

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sum from n=0 to infinity of 1/(n^6)

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

converges

Solution steps

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

Apply p-Series Test:

converges

= converges

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