Basic Analysis I — Real Analysis · Problem 2.5.4

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · series-convergence

Problem

a) Prove that if ∑n=1∞xn\sum_{n=1}^{\infty} x_n converges, then ∑n=1∞(x2n+x2n+1)\sum_{n=1}^{\infty} (x_{2n} + x_{2n+1}) also converges. b) Find an explicit example where the converse does not hold.

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