Odd numbers

Notice something

1  = 1         one odd

! + 3  = 4    two odds

1 + 3 + 5  = 9     three odds

1 + 3 + 5 + 7   =  16     four odds

So...it appears that the sum of any number, n, of  consecutive odd numbers beginning with 1 = n^2 

And there are 50 odd numbers from 1 - 100.......so the sum  is

(50)^2   = 2500