(In reply to
re: Difference Method SHIFT BY ONE by Ady TZIDON)
Ady:
You are mistaken. I wrote
"1 + 3 + ... + 2N+1 = (10) + (41) + (94) + ... + ((N+1)^2  N^2)"
Notice that 2N+1 is (N+1)^2  N^2.
Filling in also the nexttolast term gives
1 + 3 + ... + 2N+1 = (10) + (41) + (94) + ... +( N^2  (N1)^2) + ((N+1)^2  N^2)
and it is thus clear that the only term that does not cancel out is (N+1)^2 just as I wrote. Also, consider 1 + 3 = 1 + (2*1+1)  here N=1, (N+1)^2=2^2=4=1+3.

Posted by Richard
on 20040405 14:18:25 