MathDB
Miklós Schweitzer 1959- Problem 7

Source:

November 8, 2015
complex numberscollege contestsreal analysis

Problem Statement

7. Let (zn)n=1∞(z_n)_{n=1}^{\infty} be a sequence of complex numbers tending to zero. Prove that there exists a sequence (ϵn)n=1∞(\epsilon_n)_{n=1}^{\infty} (where ϵn=+1\epsilon_n = +1 or −1-1) such that the series
∑n=1∞ϵnzn\sum_{n=1}^{\infty} \epsilon_n z_n
is convergente. (F. 9)
Back to ProblemsView on AoPS