What is the sum from n=1 to infinity of n^{-1/6} ?

The sum from n=1 to infinity of n^{-1/6} is diverges

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sum from n=1 to infinity of n^{-1/6}

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

diverges

Solution steps

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

Apply exponent rule:

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

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

Apply p-Series Test:

diverges

= diverges

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\int \frac{x ^{2}}{16 - x ^{2}} d x

What is the sum from n=1 to infinity of n^{-1/6} ?
The sum from n=1 to infinity of n^{-1/6} is diverges