Wednesday, 10 May 2017

calculus - Proving that nover2n converges to 0





I'm completely clueless on this one.
I can easily calculate the limit using L'Hopital's rule, but proving that the series is converging to 0 is far more tricky.



an=n2n



Any help?


Answer



Using the fact that 2n>n2 for n>4, we have: 0an<nn2=1n.



Hence, limnan=0.



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