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# Sum of a sum of integers

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Intern
Joined: 20 Dec 2018
Posts: 1
Sum of a sum of integers  [#permalink]

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20 Dec 2018, 18:42
I was recently listening to the Christmas song "12 days of Christmas" and was wondering what the equation was for finding the total number of times objects are mentioned in the song. I've been trying all day to create a formula to come up with the sum, but I am having difficulties. Knowing (n*(n+1))/2 is the sum of integers, what is the formula for a "sum of the sum" of integers?

Senior Manager
Joined: 15 Feb 2018
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Re: Sum of a sum of integers  [#permalink]

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20 Dec 2018, 21:51
I vaguely remember the song, but I won't look it up cause it will get stuck in my head!

You should be able to use this though
https://www.math10.com/en/algebra/arith ... ssion.html
Director
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Joined: 19 Apr 2009
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Re: Sum of a sum of integers  [#permalink]

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21 Dec 2018, 01:16
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Hi icvmatthew,

These are called triangular numbers and sum of a sequence of a triangular numbers is equal to n(n+1)(n+2)/6. In case of n=12, the case for the twelve days of Christmas, we will obtain 12(13)(14)/6 = 364, almost the same as the number of days in year!

Enjoy!
Dabral
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Joined: 25 Nov 2018
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Sum of a sum of integers  [#permalink]

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21 Dec 2018, 02:12
icvmatthew wrote:
I was recently listening to the Christmas song "12 days of Christmas" and was wondering what the equation was for finding the total number of times objects are mentioned in the song. I've been trying all day to create a formula to come up with the sum, but I am having difficulties. Knowing (n*(n+1))/2 is the sum of integers, what is the formula for a "sum of the sum" of integers?

sum of integers-n:
Sum(n)= n(n+1)/2= (n^2+n)/2
Now
Sum (n^2)= n(n+1)(2n+1)/6

Sum of Sum(n)= (Sum(n^2)+ Sum(n))/2
. by solving
Sum of Sum(n)= n(n+1)(n+2)/6.

answered in a hurry, Hope u get it.
Sum of a sum of integers   [#permalink] 21 Dec 2018, 02:12
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