MathDB
Prove that c <= 1/4

Source: IMO Shortlist 1989, Problem 16, ILL 55

September 18, 2008
algebraSequencerecurrence relationInequalityIMO Shortlist

Problem Statement

The set {a0,a1,…,an} \{a_0, a_1, \ldots, a_n\} of real numbers satisfies the following conditions: (i) a_0 \equal{} a_n \equal{} 0, (ii) for 1 \leq k \leq n \minus{} 1, a_k \equal{} c \plus{} \sum^{n\minus{}1}_{i\equal{}k} a_{i\minus{}k} \cdot \left(a_i \plus{} a_{i\plus{}1} \right) Prove that c≤14n. c \leq \frac{1}{4n}.
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