Question: Problem 2: Let us first recall that if = s,

Then the sequence t_n = is also convergent and in fact

Let {a_n} be a bounded sequence (not necessarily convergent) and define

b_n =

Prove that

≤ ≤ ≤

Hint: Recall that

λ_k : = ≤ a_k ≤ for all k ≥ 1.