Question

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

Answer 1

Due to the definition of the bounded sequence, there is $M>0$ such that: $|a_n|<M$ $\forall n\in{\mathbb{N}}$. Therefore, $|\frac{a_n}{n}|<\frac{M}{n}$. We receive: $|\frac{a_n}{n}|<\frac{M}{n}\rightarrow0$. Thus, the sequence is convergent.