Winnie adds the smallest positive even numbers. Grogg adds the largest odd negative numbers. How much greater is Winnie's sum than Grogg's sum?
+23245 If they add the same number of numbers, this is an interesting problem:
(finding the sum of the smallest n positive numbers minus the sum of the largest n
negative numbers:
1 number: (2) - (-1) = 3
2 numbers: (2 + 4) - (-1 + -3) = 10
3 numbers: (2 + 4 + 6) - (-1 + -3 + -5) = 21
4 numbers: (2 + 4 + 6 + 8) - (-1 + -3 + -5 + -7) = 36
5 numbers: (2 + 4 + 6 + 8 + 10) = (-1 + -3 + -5 + -7 + -9) = 55
For a pattern: 3 = 1 · (2·1 + 1)
10 = 2 · (2·2 + 1)
21 = 3 · (2·3 + 1)
30 = 4 · (2·4 + 1)
55 = 5 · (2·5 + 1)
nth sum: Sum = n · (2·n + 1)
