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IMC 2018 P7

Source: IMC 2018 P7

July 25, 2018
real analysiscollege contestimc2018

Problem Statement

Let (an)n=0∞(a_n)_{n=0}^{\infty} be a sequence of real numbers such that a0=0a_0=0 and a_{n+1}^3=a_n^2-8  \text{for}   n=0,1,2,… Prove that the following series is convergent: ∑n=0∞∣an+1−an∣.\sum_{n=0}^{\infty}{|a_{n+1}-a_n|}.
Proposed by Orif Ibrogimov, National University of Uzbekistan
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