Problem:
Let and be the following sums of arithmetic sequences:
What is the value of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Every term in except appears in . Every term in except appears in . Therefore .
The sum has terms because it includes all even positive integers less than or equal to except for , and . The sum has the same number of terms, and every term in exceeds the corresponding term in by . Therefore .
The problems on this page are the property of the MAA's American Mathematics Competitions