Sum the series

Lost Maths Worker · science forum beginner Joined: 03 May 2005 Posts: 18

1*2*3-2^3+3*4*5-4^3+...+9999*10000*10001-10000^3.

All i have is, any help as always is appreciated;

If I split the entire series into two parts

(1*2*3+3*4*5+.........)-(2^3+4^3+.......)

The first part can be written as Summation[n(n+1)(n+2)]

Summation (n^3 + 3(n^2) + 2n)

For the second part take 2^3 common
2^3(1+2^3 + 3^3......)
2^3 Summation(n^3)

Torsten Hennig · science forum Guru Wannabe Joined: 28 Apr 2005 Posts: 136

Lost Maths Worker · science forum beginner Joined: 03 May 2005 Posts: 18

Thanks, i was also looking for a more easier solution, or more elegant, but now i wonder if there is, any help?

Julio Guerra · science forum beginner Joined: 18 Jun 2005 Posts: 1

I don't agree with you, Torsten's sollution is elegant and simple.
You have a mistake in grouping the first part to n(n+1)(n+2) and that's why
you couldn't solve it.
I was following your first steps and couldn't solve either.
Congratulations Torsten.

Regards

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