Here is the famous thing, sum of k from 1 to n is n*(n+1)/2. I'm trying to show this by recurrence equation. Then an is the sum, I have this equation: an=a(n-1)+n. It's not a*(n-1), just like this kind equations n indicates the number of the term. The charcteristic equation is r^2-r-n=0. I found the roots of r with n in it. Continue solve the coefficients became quite complicated. Am I doing right? Other good ideas?