MathDB

32

Part of 1999 National Olympiad First Round

Problems(1)

Sequence

Source: 0

4/21/2009
Let \left(a_{n} \right)_{n \equal{} 1}^{\infty } be a sequence on real numbers such that a{}_{n \plus{} 1} \equal{} a_{n} a_{n \plus{} 2} for every n≥1 n\ge 1. The number of elements in the set {an:n≥1} \left\{a_{n} : n\ge 1\right\} cannot be
<spanclass=′latex−bold′>(A)</span> 2<spanclass=′latex−bold′>(B)</span> 3<spanclass=′latex−bold′>(C)</span> 4<spanclass=′latex−bold′>(D)</span> 5<spanclass=′latex−bold′>(E)</span> None<span class='latex-bold'>(A)</span>\ 2 \qquad<span class='latex-bold'>(B)</span>\ 3 \qquad<span class='latex-bold'>(C)</span>\ 4 \qquad<span class='latex-bold'>(D)</span>\ 5 \qquad<span class='latex-bold'>(E)</span>\ \text{None}