I'm currently working on the finance problem:
If we define $I_k$ = A(k)-A(k-1) then $\sum_{k=1}^n I_k$ = A(n) - A(0)
show that this implies $\sum_{k=1}^n i_ka(k-1)$ = a(k)-1
So I know that our top equation is a telescoping sum, and every value will cancel out leaving just A(n) - A(0). Also, I know that a(n) = A(n)/A(0). Thus, we could makes a(k-1) A(k-1)/A(0) (and the same thing for the RHS). I just don't know where I should go from here in proving this equation? Any help would be appreciated.