Wednesday, 25 March 2015

calculus - Prove the series suminftyn=1frac(1)nlnn+sinn converge

How to prove this serie



n=1(1)nlnn+sinn



converge? I can't do a comparison test with the Leibniz formula for π because the series are not >0 for all n. I can't do a ratio test because I can't compute the limit, the alternating series test can't be applied, the absolute serie is not convergent. I'm out of ideas.




Any clues?

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