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.

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3 comments on “By the nth day of Christmas
  1. Scott says:

    2nd day, 2 + 1 = 3 != 2 x 3 x 4 / 6
    3rd day, 3 + 2 + 1 = 6 != 3 x 4 x 5 / 6

  2. John says:

    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

  3. Cogitoergocogitosum says:

    Does a Partridge and a Pair Tree count as two gifts, or as one?