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Here's the question:

Does the series SUM log(1+1/n) converge or diverge?

I wrote out the nth partial sums like this:

log(1+1) + log(1+1/2) + log(1+1/3)+..........+log(1+1/n)

It looks to me like the limit of the thing inside the parentheses goes to 1 as n goes to infinity, making the limit of the entire thing 0. So I say it converges.

One of my classmates says that SUM 1/n diverges, so this one does too. I can't disagree with him, but I fail to see the relevance.

I'm confused. Any clarification will be appreciated.

CC

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# Homework Help: Infinite series question

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