Friday, December 1, 2017

convergence divergence - Seeking a rigorous proof for a limit




Prove thatlimnln(13n)n=0



I knew that this is the indeterminate form 0/(Actually it isn't, so I made a dumb mistake) that should be zero but was unable to prove it. I haven't tried using the definition yet because I feel that's too cumbersome?


Answer



Note that the limit is not an indeterminate form, indeed:



ln(13n)ln1=0ln(13n)n0+=0


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