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 !
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.
L'H˘pital'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