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Turkey NMO 2000 1st Round - P36 (Algebra)

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July 25, 2012

Problem Statement

xn+1=(1+2n)xn+4nx_{n+1}= \left ( 1+\frac2n \right )x_n+\frac4n, for every positive integer nn. If x1=−1x_1=-1, what is x2000x_{2000}?
<spanclass=′latex−bold′>(A)</span> 1999998<spanclass=′latex−bold′>(B)</span> 2000998<spanclass=′latex−bold′>(C)</span> 2009998<spanclass=′latex−bold′>(D)</span> 2000008<spanclass=′latex−bold′>(E)</span> 1999999 <span class='latex-bold'>(A)</span>\ 1999998 \qquad<span class='latex-bold'>(B)</span>\ 2000998 \qquad<span class='latex-bold'>(C)</span>\ 2009998 \qquad<span class='latex-bold'>(D)</span>\ 2000008 \qquad<span class='latex-bold'>(E)</span>\ 1999999
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