# Sum the series

• May 21st 2005, 11:37 PM
cornoth
Sum the series
Sum the series:

1*2*3-2^3+3*4*5-4^3+...+9999*10000*10001-10000^3.
• May 22nd 2005, 12:11 AM
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)
I hope you can expand for the individual summations.

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

Hope you can take it from here.
• May 23rd 2005, 02:19 AM
cornoth
- 25,005,000 Correct?
Each 'group' starts from -2, then add -3+....+-9999+-10000
• Aug 24th 2005, 08:53 PM
ardnas
Can someone explain why the summation is like that? I still don't get it.
• Aug 25th 2005, 06:52 AM
Can you please explain which part of the summation you didnt understand??
• Aug 25th 2005, 06:57 AM
ardnas
For the second part take 2^3 common
2^3(1+2^3 + 3^3......)
2^3 Summation(n^3)

Then do I add the two summation together? And should I put 5000 for n?
• Aug 25th 2005, 07:24 AM