Question 199733
This is one of those cases where working on a small set of numbers and finding a pattern can really help. So instead of going to 100, do the problem up to 10.

Take the numbers in pairs. First pair is (1 and 2), 2-1 = 1
Now take (3 and 4) 4-3 = 1  
next (5 and 6) 6-5 =1  hmmm, I am seeing a pattern here
7 and 8 --> 1 again
9 ,10 ---> 1 again
We can see that each pair adds one to the sum. 
With an upper limit of 10, we have 5 pairs. So the sum is 10/2 = 5

If you extrapolate from there, you would say "divide the upper limit by 2".
Test it by trying the pattern to 20. Does that work?
Yes it does.
The pattern works, so the answer is 100/2 = 50