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P36 [Algebra] - Turkish NMO 1st Round - 2003

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May 31, 2014

Problem Statement

a1,a2,⋯ ,a2003a_1,a_2, \cdots , a_{2003} are integers such that ∣a1∣=1|a_1| = 1 and ∣ai+1∣=∣ai+1∣|a_{i+1}|=|a_i+1| (1≤i≤2002)(1\leq i \leq 2002). What is the minimal value of ∣a1+a2+⋯+a2003∣|a_1+a_2+\cdots + a_{2003}|?
<spanclass=′latex−bold′>(A)</span> 4<spanclass=′latex−bold′>(B)</span> 34<spanclass=′latex−bold′>(C)</span> 56<spanclass=′latex−bold′>(D)</span> 65<spanclass=′latex−bold′>(E)</span> None of the preceding <span class='latex-bold'>(A)</span>\ 4 \qquad<span class='latex-bold'>(B)</span>\ 34 \qquad<span class='latex-bold'>(C)</span>\ 56 \qquad<span class='latex-bold'>(D)</span>\ 65 \qquad<span class='latex-bold'>(E)</span>\ \text{None of the preceding}
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