Re: recurrence/proof help please
On 11-04-2005 15:07, jimbo wrote:
I am in the process of solving a recurrence in a proof and I've hit a
snag. I currently have:
the summation of ((N-L+1)(L-1)) from L=2 to N.
I need to reduce this to something like
the summation of ((NL-L^2)) from L=1 to N-1.
but I can't quite figure out how to get there.
Anyone have any ideas?
The first summation is:
(N - 1)*1 + (N - 2)*2 + (N - 3)*3 + ... + 1*(N - 1)
which is equal to
(N*1 - 1^2) + (N*2 - 2^2) + (N*3 - 3^3) + ... + (N*(N - 1) - (N - 1)^2)
whereas the second one is
(N*1 - 1^2) + (N*2 - 2^2) + (N*3 - 3^3) + ... + (N*(N - 1) - (N - 1)^2)
Can you see a difference? I can't.
Best regards,
Jose Carlos Santos
.
