Prove or disprove series – math.stackexchange.com

Prove or disprove series – math.stackexchange.com

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Assume $\sum_{n=k}^{\infty} a_n$ converges. Then $\sum_{n=k}^{\infty} a_n \cdot a_{n+2}$ converges? I think I should disprove it, because $\sum_{n=k}^{\infty} a_{n+2}$ might diverge but I can't find ...

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