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Wait wasn't it the reciprocal in the paper?

Source: India TST 2023 Day 2 P1

July 9, 2023
algebrainequalities

Problem Statement

Let Z≥0\mathbb{Z}_{\ge 0} be the set of non-negative integers and R+\mathbb{R}^+ be the set of positive real numbers. Let f:Z≥02→R+f: \mathbb{Z}_{\ge 0}^2 \rightarrow \mathbb{R}^+ be a function such that f(0,k)=2kf(0, k) = 2^k and f(k,0)=1f(k, 0) = 1 for all integers k≥0k \ge 0, and f(m,n)=2f(m−1,n)⋅f(m,n−1)f(m−1,n)+f(m,n−1)f(m, n) = \frac{2f(m-1, n) \cdot f(m, n-1)}{f(m-1, n)+f(m, n-1)} for all integers m,n≥1m, n \ge 1. Prove that f(99,99)<1.99f(99, 99)<1.99.
Proposed by Navilarekallu Tejaswi
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