Basic Analysis I — Real Analysis · Problem 2.6.3

Sequences and Series — Jiri Lebl

Mathematics — Real Analysis · series-rearrangements

Problem

(Challenging): Let ∑n=1∞an\sum_{n=1}^{\infty} a_n be conditionally convergent. Show that given an arbitrary x∈Rx \in \mathbb{R} there exists a rearrangement of ∑n=1∞an\sum_{n=1}^{\infty} a_n such that the rearranged series converges to xx. Hint: See Example 2.6.4.

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