MathDB

2010 China Second Round,test 2,problem 3

Source:

February 11, 2012

inequalities proposedinequalities

Problem Statement

let

n>2

be a fixed integer.positive reals

a_i\le 1

(for all

1\le i\le n

).for all

k=1,2,...,n

,let

A_k=\frac{\sum_{i=1}^{k}a_i}{k}

prove that

|\sum_{k=1}^{n}a_k-\sum_{k=1}^{n}A_k|<\frac{n-1}{2}