MathDB

3

Part of 1990 Baltic Way

Problems(1)

Can the sequence become negative at a specified time?

Source:

4/19/2013
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?