International Mathematics Competition for University Students

July 22 – 28 2018, Blagoevgrad, Bulgaria

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Day 1
    Problem 1
    Problem 2
    Problem 3
    Problem 4
    Problem 5

Day 2
    Problem 6
    Problem 7
    Problem 8
    Problem 9
    Problem 10

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    Day 1 questions
    Day 1 solutions
    Day 2 questions
    Day 2 solutions
    Closing Ceremony
        Presentation

Official IMC site

Problem 7

Problem 7. Let \(\displaystyle (a_n)_{n=0}^\infty\) be a sequence of real numbers such that \(\displaystyle a_0=0\) and

\(\displaystyle a_{n+1}^3=a_n^2-8 \quad \text{for} \quad n=0,1,2,\ldots \)

Prove that the following series is convergent:

\(\displaystyle \sum_{n=0}^\infty|a_{n+1}-a_n|. \)\(\displaystyle (1) \)

(Proposed by Orif Ibrogimov, National University of Uzbekistan)

  Hint    Solution