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Infinite Serieshard
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If ∑n=0∞an=A\sum_{n=0}^{\infty} a_n = A∑n=0∞​an​=A and ∑n=0∞bn=B\sum_{n=0}^{\infty} b_n = B∑n=0∞​bn​=B both converge absolutely, what is true about their Cauchy product ∑n=0∞cn\sum_{n=0}^{\infty} c_n∑n=0∞​cn​ where cn=∑k=0nakbn−kc_n = \sum_{k=0}^{n} a_k b_{n-k}cn​=∑k=0n​ak​bn−k​?