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November 12th, 2017, 02:00 PM   #1
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How to show the following limit is 0?

I have the series 1/(n*(-1)^n). I believe the limit is 0, but I'm not sure how to show that.

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Last edited by Mathmatizer; November 12th, 2017 at 02:02 PM.
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November 12th, 2017, 03:22 PM   #2
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It's the alternating harmonic series isn't it? Convergence guaranteed because the sequence $|a_n|$ is decreasing and $a_n$ is alternating.
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November 12th, 2017, 03:53 PM   #3
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The sum is ln 2.

https://en.wikipedia.org/wiki/Harmon...armonic_series

ps -- OP said series. The limit of the sequence is of course 0.
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Last edited by Maschke; November 12th, 2017 at 04:49 PM.
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