SOLUTION: The sum of the positive odd integers less than 100 is subtracted from the sum of the positive even integers less than or equal to 100. What is the resulting difference?

Question 199733: The sum of the positive odd integers less than 100 is subtracted from the sum of the positive even integers less than or equal to 100. What is the resulting difference?
Answer by vleith(2983) (Show Source): You can put this solution on YOUR website!
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

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