Sum and Difference
Algebra
Level
pending
Find the value when the sum of all positive odd integers less than 1000 is subtracted from the sum of all even positive integers less than 1001.
The answer is 500.
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1 solution
f ( x ) = 2 + 4 + 6 + 8 + 1 0 + 1 2 + . . . . + 1 0 0 0 p ( x ) = 1 + 3 + 5 + 7 + 9 + 1 1 + 1 3 + . . . . + 9 9 9
To find : f ( x ) − p ( x )
f ( x ) = 2 + 4 + 6 + 8 + 1 0 + 1 2 + . . . . . + 1 0 0 0 ( − ) p ( x ) = 3 + 5 + 7 + 9 + 1 1 + 1 3 + . . . . . + 9 9 9
That is equal to
f ( x ) = 2 + 4 + 6 + 8 + 1 0 + 1 2 + . . . . . + 1 0 0 0 p ( x ) = − 1 − 3 − 5 − 7 − 9 − 1 1 − . . . . . − 9 9 9 f ( x ) − p ( x ) = 1 + 1 + 1 + 1 + 1 + 1 + . . . . . + 1 = 5 0 0