Gauss' method, supposedly at the age of 5 according to the story ...
Consider pairs:
1 + 100 = 101
2 + 99 = 101
3 + 98 = 101
4 + 97 = 101
5 + 96 = 101
Each pair sums to 101, and there are (100/2) = 50 of them.
So their grand sum is (101 x 50) = 5050.
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99, 100, and 101
The integers are 99, 100 and 101. There is also a set of consecutive even integers whose sum is 300. That set is 98, 100 and 102.
The sum of any two consecutive integers must be an odd number. So this question is incorrect.
-3,-4,-5
find the two consecutive odd integers with a sum of 152