I have question which to show that sum(1/n)log[1+(1/n)] is convergent. I don't think i can use integral or ratio or raabe's test. I am guessing I have to use limit comparison test ??? Help me !

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- May 13th 2011, 07:28 AMmathsohardconvergence test
I have question which to show that sum(1/n)log[1+(1/n)] is convergent. I don't think i can use integral or ratio or raabe's test. I am guessing I have to use limit comparison test ??? Help me !

- May 13th 2011, 07:33 AMTheEmptySet
- May 13th 2011, 07:40 AMmathsohard
I haven't learned l'Hospitals rule yet lol is that the only way ???

- May 13th 2011, 07:48 AMTheEmptySet
Well if you do the limit comparison you will need to calculate the limit

This is an indeterminate form of infinity times zero. What methods have you learned to resolve these types of limits? The only other method I can think of is to use a Taylor series expansion, but that is usually covered after the topics you are learning right now. - May 13th 2011, 08:29 AMmathsohard
Well can you show me how to do with l'Hospitals rule then???

- May 13th 2011, 08:50 AMTheEmptySet
Here is a link to the theorem:

L'Hôpital's rule - Wikipedia, the free encyclopedia

This is of the form zero over zero so we take the derivative of the numerator and denominator to get