Suppose that (sn)neN and (tn)neN are sequences and assume that (tn) converges. (a) Suppose that there exists a constant C> 0 such that sn - Sm] ≤ Ctn - tm for all n, me N. Prove that (sn) converges. (b) Let tn (-1). Then (tn) converges. Give an example of a sequence (sn) that does not converge for which sn - Sn+1| ≤ |tn − tn+1] for all n. =

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