Question: (a) Prove that the sequencea n = 1 + (1/2) 1/3 + (1/3) 1/3 + ... + (1/n) 1/3 is NOT a Cauchy sequence. Only

(a) Prove that the sequencean = 1 + (1/2)1/3 + (1/3)1/3+ ... + (1/n)1/3 is NOT a Cauchy sequence. Only use thedefinitionof Cauchy sequences.

(b) Is the sequence(an) convergent? Explain your answer.

Definition: A sequence an is a Cauchy sequence if for each > 0 there is a cut-off integer N such that if m,n >= N, then |am-an| <

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