Question: Suppose that series ( an is conditionally convergent. (a) Prove that the series (n2 an is divergent. (b) Conditional convergence of (an is not enough

Suppose that series ( an is conditionally convergent.
(a) Prove that the series (n2 an is divergent.
(b) Conditional convergence of (an is not enough to determine whether (nan is convergent. Show this by giving an example of a conditionally convergent series such that (nan converges and an example where (nan diverges.

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