- #1
pupeye11
- 100
- 0
Homework Statement
Find integers a,b, and c such that [tex]m^{3} = a*nCr(m,3)+b*nCr(m,2)+c*nCr(m,1)[/tex] for all m. Then sum the series [tex]1^3+2^3+3^3+...+n^3[/tex]
Homework Equations
I think I need to use [tex]m^{3} = a*nCr(m,3)+b*nCr(m,2)+c*nCr(m,1)[/tex] and [tex]nCr(n+1,k+1)=nCr(0,k)+nCr(1,k)+...+nCr(n-1,k)+nCr(n,k)[/tex] to be able to sum the series but I am not sure
The Attempt at a Solution
I am not really sure how to get started, I originally thought that a=3, b=2, and c=1 but the more I think about it that doesn't seem right. I believe that if it was just [tex]m^2=a*nCr(m,2)+b*nCr(m,1)[/tex] then a=2 and b=1 but I am not sure why, I just know it works.