I'm having trouble with this equation mainly because it has a couple of odd things with it, and its these that have thrown me off as i'm not to sure how to tackle them. The equation is:
n - 1 SUM ( n - i) = n(n - 1)/2 i = 1
Heres my method of working it out so far:
Assume a baseline of i = 1. (1 - 1) on LHS = 0 1(1 - 1)/ 2 on RHS = 0 Thus the equation can be solved. Here we test if it also works with (n + 1) which would be (n - 1 + 1)? = n. LHS: So (n - i) = ((n + 1) + n) = 2n + n n(n - 1)/2 + (2n + n) = (n^2 - n + 6n) / 2 RHS: Basically add 1 to every n available. (n + 1)((n + 1) - 1)/2 = (n^2 + n)/2 Thus, Since LHS != RHS Its not true?
I'm not really to sure. Here are my main problems:
With the (n - 1) at the top of the SUM, do I add 1 for every iteration or minus 1 so it becomes (n - 2)?
Also, with the (n - i), for the LHS what does that become? because I dont think (2n + n) is correct.
Thanks for all the help! I've been stuck on this one for a while with all the others being pretty simple kinda. :)