Question

What is the sum of all the odd #s between 100 & 200??

Answer 1

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