MathDB

7

Part of 2018 IMC

Problems(1)

IMC 2018 P7

Source: IMC 2018 P7

7/25/2018
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
real analysiscollege contestimc2018