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Can the sequence become negative at a specified time?

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April 19, 2013

Problem Statement

Given a0>0a_0 > 0 and c>0c > 0, the sequence (an)(a_n) is defined by a_{n+1}=\frac{a_n+c}{1-ca_n} \text{for }n=1,2,\dots Is it possible that a0,a1,…,a1989a_0, a_1, \dots , a_{1989} are all positive but a1990a_{1990} is negative?
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