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(Solved): 15.6(c). Give an example of a convergent series \( \sum a_{n} \) for which \( \sum a_{n}^{2} \) di ...
15.6(c). Give an example of a convergent series \( \sum a_{n} \) for which \( \sum a_{n}^{2} \) diverges. Prove that if \( a_{n} \geq 0 \) for all \( n \geq 1 \), then \( \sum a_{n}^{2} \) converges. [4]