Math Is Fun Forum

sumabala

Member

Registered: 2014-11-16

Posts: 1

finding nth row total

Sir,  the question is what is the total of nth row of the followingdistribution of the natural numbers.
                          1
                         2  3
                      4    5   6
                   7    8    9    10
                ... ..   ...  ...   ....
          ...  ..   ...   .....   ....   ....
please guide me with a formula that can be used in this.---Regards--Balaji

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: finding nth row total

Hi;

This problem has already been solved:

a(n)=(1/6)*(3*n^3+3*n)

http://oeis.org/search?q=1%2C5%2C15%2C3 … &go=Search

Post back if you can not wade through their work.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Olinguito

Member

Registered: 2014-08-12

Posts: 649

Re: finding nth row total

Let T(n) represent the nth triangular number; then the nth row is

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Hence the sum is

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Bassaricyon neblina