By the nth day of Christmas

By the nth day of Christmas, my true love had sent to me n(n+1)(n+2)/6 gifts.

Explanation and proof here.

3 thoughts on “By the nth day of Christmas

  1. Scott:

    On the nth day, there are n + (n-1) + … + 2 + 1 = n(n+1)/2 new gifts, and a cumulative total of n(n+1)(n+2)/6 gifts.

    2nd day, (2 + 1) + 1 = 4 = 2*3*4/6
    3rd day, (3+ 2 + 1) + (2 + 1) + 1 = 10 = 3*4*5/6

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