And help with this would be appreciated! Prove that if the series, ∑_{n=1}^{infinity }(n*s_{n}) converges, then s_{n} tends to 0 as n tends to infinity.
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Hint: If $\displaystyle \sum\limits_{n = 1}^\infty {{a_n}} $ converges then we know that $\displaystyle \left( {{a_n}} \right) \to 0$.
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