IMO 2006 Shortlist N3
The sequence f(1),f(2),f(3),... is defined by f(n) = n jn k + jn k + ··· + jn n k , where bxc denotes the integer part...
Category: Number Theory
Problem
The sequence f(1),f(2),f(3),... is defined by f(n) = n jn k + jn k
- ··· + jn n k , where bxc denotes the integer part of x. (a) Prove that f(n + 1) > f(n) infinitely often. (b) Prove that f(n + 1) < f(n) infinitely often. (South Africa)