Sum the series:
1*2*3-2^3+3*4*5-4^3+...+9999*10000*10001-10000^3.
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.
1^3 + 2^3 + 3^3 + 4^3 +........5000^3
Each number can be written as n^3.
Since we are adding the numbers we take Summation(n^3)
Correct n=5000 since we took 2 common.
There's a negative sign between the two series so techincally you are subtracting one from the other.