We have an infinite sequence of integers {xn}, such that x1=1, and, for all n≥1, it holds that xn<xn+1≤2n. Prove that there are two terms of the sequence,xr and xs, such that xr−xs=2018.
Source: Mathematics Regional Olympiad of Mexico Northeast 2018 P4
Tags: algebra, Sequence
We have an infinite sequence of integers {xn}, such that x1=1, and, for all n≥1, it holds that xn<xn+1≤2n. Prove that there are two terms of the sequence,xr and xs, such that xr−xs=2018.