MathDB

n-variable inequality

Source: 2015 IMO Shortlist A1, Original 2015 IMO #5

July 7, 2016

algebraIMO ShortlistSequenceInequalityinduction

Problem Statement

Suppose that a sequence

a_1,a_2,\ldots

of positive real numbers satisfies

a_{k+1}\geq\frac{ka_k}{a_k^2+(k-1)}

for every positive integer

k

. Prove that

a_1+a_2+\ldots+a_n\geq n

for every

n\geq2