MathDB

sum of a_i = (a_1 + a_2 +... + a_n)/2

Source: 6th QEDMO problem 8 (22. - 29. 8. 2009) https://artofproblemsolving.com/community/c1512515_qedmo_200507

May 8, 2021

algebraSum

Problem Statement

Given

n

integers

a_1, a_2, ..., a_n

, which

a_1 = 1

and

a_i \le a_{i + 1} \le 2a_i

for each

i \in \{1,2,...,n-1\}

. Prove that if

a_1 + a_2 +... + a_n

is even, you do select some of the numbers so that their sum equals

\frac{a_1 + a_2 +... + a_n}{2}