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# Alternating and diverging series- use Leibniz test? Watch

1. I'm asked to find whether this sum (absolutely)Converges or Diverges

when .

I know it's an alternating series since because of and that , which means the series diverges since is obviously increasing.

But how can I use Leibniz test(aka Alternating Series Test) to show this series is divergent when the Leibniz test is used to show a series converging?

I could use the Divergence test since doesn't equal .
2. Can you remember the conditions that need to be met in order to show that a series converges using the leibniz theorem?
3. Surely for the Leibniz test to be applicable, you'd need where we define , which is clearly not true?
4. Hmm, I'm thinking of writing the same thing too...

Since , according to Leinbnitz test is not converging, hen the series is sdivergent and alternating series.
5. For to be convergent, we must have . But this isn't the case (in particular, |b_n| -> e so b_n doesn't tend to 0), so the series does not converge. Leibniz's test is a test for convergence, it doesn't show divergence.
6. So is there any point of using the Leibnitz test whatsoever for this problem? We already know the limit goes to so the series must be diverging...
7. (Original post by TheNihilist)
So is there any point of using the Leibnitz test whatsoever for this problem? We already know the limit goes to so the series must be diverging...
Nope, no point. Also, |b_n| goes to e, b_n doesn't tend to anything.

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