Basic Analysis I — Real Analysis · Problem 2.6.2

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · cauchy-product

Problem

Suppose both ∑n=0∞an\sum_{n=0}^{\infty} a_n and ∑n=0∞bn\sum_{n=0}^{\infty} b_n converge absolutely. Show that the product series, ∑n=0∞cn\sum_{n=0}^{\infty} c_n where cn=a0bn+a1bn−1+⋯+anb0c_n = a_0 b_n + a_1 b_{n-1} + \cdots + a_n b_0, also converges absolutely.

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