This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

Tags were heavily modified to better represent problems.

AND
OR
NO

Found problems: 1

2016 ISI Entrance Examination, 8
Suppose that $(a_n)_{n\geq 1}$ is a sequence of real numbers satisfying $a_{n+1} = \frac{3a_n}{2+a_n}$. (i) Suppose $0 < a_1 <1$, then prove that the sequence $a_n$ is increasing and hence show that $\lim_{n \to \infty} a_n =1$. (ii) Suppose $ a_1 >1$, then prove that the sequence $a_n$ is decreasing and hence show that $\lim_{n \to \infty} a_n =1$.
real analysis 1 sequence real analysis convergence algebra mathematical induction recurrence relations sequences