What is the sum from n=0 to infinity of 1/(n^{3/2)} ?

The sum from n=0 to infinity of 1/(n^{3/2)} is converges

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sum from n=0 to infinity of 1/(n^{3/2)}

n = 0 \sum \infty \frac{1}{n ^{\frac{3}{2}}}

converges

Solution steps

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

Apply p-Series Test:

converges

= converges

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What is the sum from n=0 to infinity of 1/(n^{3/2)} ?
The sum from n=0 to infinity of 1/(n^{3/2)} is converges