(Q3) (a) Prove that if (an) and (bn) are sequences such that (an) converges and (an-bn) converges, then (bn) converges. (b) Suppose that (n) is any converging sequence and (yn) is any diverg- ing sequence. Can you say in general whether (n - Un) converges or diverges? Justify your answer. [Hint: Use the previous part.]

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