MathDB
a_{1998} > 63 if a_n =a_{n-1} + 1/ a_{n-1}

Source: Portugal OPM 1998 p6

May 18, 2024
inequalitiesalgebraSequencerecurrence relation

Problem Statement

Let a0a_0 be a positive real number and consider the general term sequence ana_n defined by an=an−1+1an−1   n=1,2,3,...a_n =a_{n-1} + \frac{1}{a_{n-1}} \,\,\, n=1,2,3,... Prove that a1998>63a_{1998} > 63.
Back to ProblemsView on AoPS