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Infinite Serieseasy
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If Sn=∑i=1naiS_n = \sum_{i=1}^n a_iSn​=∑i=1n​ai​ is the sequence of partial sums of a series, what is the value of ∑n=1∞an\sum_{n=1}^{\infty} a_n∑n=1∞​an​ if lim⁡n→∞Sn=L\lim_{n \to \infty} S_n = Llimn→∞​Sn​=L?