What is the sum from n=1 to infinity of 1/(n^{11/2)} ?

The sum from n=1 to infinity of 1/(n^{11/2)} is converges

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sum from n=1 to infinity of 1/(n^{11/2)}

n = 1 \sum \infty \frac{1}{n ^{\frac{11}{2}}}

converges

Solution steps

n = 1 \sum \infty \frac{1}{n ^{\frac{11}{2}}}

Apply p-Series Test:

converges

= converges

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

n = 0 \sum \infty \frac{4}{5 n}

n = 1 \sum \infty n - 2

n = 3 \sum \infty \frac{6}{( n ^{2} - 1 )}

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

What is the sum from n=1 to infinity of 1/(n^{11/2)} ?
The sum from n=1 to infinity of 1/(n^{11/2)} is converges