What is the sum from n=0 to infinity of n^{-9} ?

The sum from n=0 to infinity of n^{-9} is converges

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sum from n=0 to infinity of n^{-9}

n = 0 \sum \infty n^{- 9}

converges

Solution steps

n = 1 \sum \infty n^{- 9}

Apply exponent rule:

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

= n = 1 \sum \infty \frac{1}{n ^{9}}

Apply p-Series Test:

converges

= converges

n = 1 \sum \infty (\frac{4}{9})^{n}

n = 0 \sum \infty n^{- n}

n = 1 \sum \infty (\frac{π}{e})^{n}

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

n = 1 \sum \infty \frac{n + 5}{n + 4}

What is the sum from n=0 to infinity of n^{-9} ?
The sum from n=0 to infinity of n^{-9} is converges