MathDB

8

Part of 2009 QEDMO 6th

Problems(1)

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

5/8/2021
Given nn integers a1,a2,...,ana_1, a_2, ..., a_n, which a1=1a_1 = 1 and ai≤ai+1≤2aia_i \le a_{i + 1} \le 2a_i for each i∈{1,2,...,n−1}i \in \{1,2,...,n-1\} . Prove that if a1+a2+...+ana_1 + a_2 +... + a_n is even, you do select some of the numbers so that their sum equals a1+a2+...+an2\frac{a_1 + a_2 +... + a_n}{2} .
algebraSum