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The sum of the even numbers is (26 + 28 + ... + 100);

The sum of the odd numbers is (25 + 27 + ... + 99)

Their difference is:

(26 + 28 + ... + 100) - (25 + 27 + ... + 99) = (26 - 25) + (28 - 27) + ... + (100 - 99)

= 1 + 1 + ... + 1

There are (100 - 26) ÷ 2 + 1 = 38 terms above which are all 1; their sum is 38 x 1 = 38.

So the difference of the sum of all even numbers and all odd numbers 25-100 is 38.

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โˆ™ 2013-12-07 12:44:14
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Q: What is the difference between the sum of all even numbers and odd numbers from 25 to 100?
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