This is an arithmetic sum with a constant subtracted.
Or written in longhand,
Note that there are 101 terms inside the parentheses.
Note also that pairs of terms starting from opposite ends (50 of them) always add up to 100. The middle term, 50, stands alone with no counterpart. Rearranging,
Written another way,
But since
, and the 50s cancel out, this reduces to,
The answer is 5000.
This is a trivial case of the general formula for sums
Where a=0, d=1, and n=101
(minus 50 equals 5000)