Answer to Question #203182 in Real Analysis for Rajkumar

Question #203182

Prove that the sequence {an /n } is convergent where { an } is a bounded sequence.



1
Expert's answer
2022-02-04T11:56:07-0500

Suppose that the sequence ana_n is bounded. It means that there is M>0M>0 such that an<M|a_n|<M n\forall n. Therefore, ann<Mn|\frac{a_n}{n}|<\frac{M}{n}. Since Mn0\frac{M}{n}\rightarrow0, nn\rightarrow\infty, ann0|\frac{a_n}{n}|\rightarrow0, n.n\rightarrow\infty.


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