
How Many Gifts In 12 Days Of Christmas Formula
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How Many Gifts In 12 Days Of Christmas Formula
I tried to forget about it, but couldnt. Thanks for doing it. Peter says: 20 Dec 2013 at 11:47 am [Comment permalink] very cool, not sure if your students are at a level where they know about taylor series or combinatorics, but the number of presents from n days of giving is also the n'th coefficient in the taylor expansion of: x/(1x)^4 just learned about combinatorics this past semester, great stuff!! . I didnt figure it out during the drive, and then after getting back to college I still failed to find the solution, so I gave up and asked a math professor. 2B = n(n+1)(2n+1)/6 + n(n+1)/2 We multiply the second part of the sum by 3/3: 2B = n(n+1)(2n+1)/6 + 3n(n+1)/6, or: 2B = [n(n+1)(2n+1) + 3n(n+1)] / 6, or: B = [n(n+1)(2n+1) + 3n(n+1)] / 12. = 1*2/2 + 2*3/2 + 3*4/2 + + n*(n+1)/2. Making all 364 gifts in total would take a lot of time, and even just making the 78 gifts of the last verse will be a [&] . + If we imagine that the singer had continued singing for 20 days they would have received: = 210gifts on the 20th day! Running total of gifts Let us now look at the running total of gifts at the end of day The running total will be equal to where stands for the th triangular number. Mike says: 3 Jul 2009 at 8:43 am [Comment permalink] Awesome, i encountered this problem in haven of all places and i came up with the long way of figuring it out (noone told me it) but a friend of mine used the method above (or something similar), she told me if you picture it, it forms like a triangle and i just thought to myself i'm not even going there i was bewildered but fascinated but since then i have been looking at different maths problems as the whole magic of maths has got to me lol. cf4ac695ea
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