Posted by Gilbert on Wednesday, November 28, 2012 at 11:56am.
note that the sum of the first n odd numbers is n^2
1=1
1+3=4
1+3+5=9
...
There are 50 odds below 100
There are 100 odds below 200
sum of 1st 50 odds is 50^2
sum of 1st 100 odds is 100^2
sum of odds between 100 and 200 is thus 100^2-50^2 = 7500