# 1956 AHSME Problems/Problem 25

## Problem 25

The sum of all numbers of the form , where takes on integral values from to is:

## Solution

The sum of the odd integers from to is . However, in this problem, the sum is instead , starting at rather than . To rewrite this, we note that is less than for every we add, so for 's, we subtract , giving us ,which factors as .