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
.