What is the sum from n=1 to infinity of (-1)^nn^{-1} ?

The sum from n=1 to infinity of (-1)^nn^{-1} is converges

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sum from n=1 to infinity of (-1)^nn^{-1}

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

converges

Solution steps

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

n^{- 1} = \frac{1}{n}

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

Apply Alternating Series Test:

converges

= converges

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What is the sum from n=1 to infinity of (-1)^nn^{-1} ?
The sum from n=1 to infinity of (-1)^nn^{-1} is converges