Prove that the sequence {an /n } is convergent where { an } is a bounded sequence.
Suppose that the sequence ana_nan is bounded. It means that there is M>0M>0M>0 such that ∣an∣<M|a_n|<M∣an∣<M ∀n\forall n∀n. Therefore, ∣ann∣<Mn|\frac{a_n}{n}|<\frac{M}{n}∣nan∣<nM. Since Mn→0\frac{M}{n}\rightarrow0nM→0, n→∞n\rightarrow\inftyn→∞, ∣ann∣→0|\frac{a_n}{n}|\rightarrow0∣nan∣→0, n→∞.n\rightarrow\infty.n→∞.
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