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Omni-MATH / Given a₀>0 and c>0, the sequence (a_(n)) is defined by

Problem

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problem

Given a0>0a_0 > 0 and c>0c > 0, the sequence (an)(a_n) is defined by an+1=an+c1−canfor n=1,2,…a_{n+1}=\frac{a_n+c}{1-ca_n}\quad\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?
Plain-text mathematical notation (without MathML)
Given a₀>0 and c>0, the sequence (a_(n)) is defined by
a_(n+1)=(a_(n)+c)/(1−ca_(n)) for n=1,2,…
Is it possible that a₀,a₁,…,a₁₉₈₉ are all positive but a₁₉₉₀ is negative?
Original LaTeX notation
Given $a_0 > 0$ and $c > 0$, the sequence $(a_n)$ is defined by
\[a_{n+1}=\frac{a_n+c}{1-ca_n}\quad\text{for }n=1,2,\dots\]
Is it possible that $a_0, a_1, \dots , a_{1989}$ are all positive but $a_{1990}$ is negative?

Discussion

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Source and history

task_id
05ee45df-cb16-5e68-895d-366b6e863e46
task_key
test--05ee45df-cb16-5e68-895d-366b6e863e46
task_revision_id
1
config / split
/ test

Official source

initial import