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Infinite Seriesmedium
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Given that the series ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞​an​ converges where an>0a_n > 0an​>0, what can be definitively concluded about the series ∑n=1∞anan+1\sum_{n=1}^{\infty} \sqrt{a_n a_{n+1}}∑n=1∞​an​an+1​​?