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The sum of the squares of the first 100 natural numbers [1..100] is 338350, while the sum of the first 100 natural numbers squared is 25502500.
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.
There are no two consecutive even numbers whose sum is 100. It is easily proved.
There are infinitely many pairs of numbers whose difference is equal to the sum of 538 and 259 (which is 797). One such pair is 420 and 1217. Another pair is 0 and 797.
5
The two numbers are 50 and 63. Their sum is 113 and they have a difference of 13.
The sum of the numbers 1 to 100 is 5050.
The numbers are 53 and 47
25 and 11
The sum of the squares of the first 100 natural numbers [1..100] is 338350, while the sum of the first 100 natural numbers squared is 25502500.
Finding the sum is adding two numbers together. The product comes from multiplying them together. Therefore, the sum of 100 and 100 is 200. The product of 100 and 100 is 10,000. Thus, the difference (which comes from subtracting two numbers) between the two is 9,800.
The numbers are 51.5 and 48.5
The numbers are 53 and 47
The sum of 538 and 259 is 797. there are no two numbers among those given with a difference of 797.
65 and 35
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.
The numbers 100 and 66, since 100+66=166 and 100-66=34.