What is the sum from n=1 to infinity of (-1^n)/(n^5) ?

The sum from n=1 to infinity of (-1^n)/(n^5) is converges

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sum from n=1 to infinity of (-1^n)/(n^5)

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

converges

Solution steps

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

Apply the constant multiplication rule:

\sum c \cdot a_{n} = c \cdot \sum a_{n}

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

Simplify

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

Apply p-Series Test:

converges

= - converges

= converges

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What is the sum from n=1 to infinity of (-1^n)/(n^5) ?
The sum from n=1 to infinity of (-1^n)/(n^5) is converges