Help with summations.
Hello, I am having trouble solving this summation:
Summation from j=i to N-1 of: (j-i+1)
The answer is said to be: ((N-i+1)(N-i)) / 2
I have tried separating the summation into three separate summations consisting of:
(summation from j=i to N-1 of j) - (summation from j=i to N-1 of i) + (summation from j=i to N-1 of 1)
This leads me to: ((N+2)(N-1) / 2) - i(N-i-1)
But that is obviously not the right answer (unless I am simplifying something incorrectly). Please let me know what I am doing wrong. I have been stuck on this problem for a while now and I need to move on with my homework. Thank you very much for your help.