What is the sum from n=1 to infinity of 1/(n^{pi/4)} ?

The sum from n=1 to infinity of 1/(n^{pi/4)} is diverges

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sum from n=1 to infinity of 1/(n^{pi/4)}

n = 1 \sum \infty \frac{1}{n ^{\frac{π}{4}}}

diverges

Solution steps

n = 1 \sum \infty \frac{1}{n ^{\frac{π}{4}}}

Apply p-Series Test:

diverges

= diverges

n = 0 \sum \infty (\frac{7}{10})^{n}

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

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

n = 0 \sum \infty \frac{5}{1 1 ^{n}}

n = 1 \sum \infty (\frac{8 π}{9})^{n}

What is the sum from n=1 to infinity of 1/(n^{pi/4)} ?
The sum from n=1 to infinity of 1/(n^{pi/4)} is diverges