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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?

 Feb 24, 2022
 #1
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The answer is 1425.

 Feb 24, 2022
 #2
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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)

 Feb 25, 2022

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