I'm having trouble showing how to solve this problem in particular the part where it asks To Show that the following pseudo-code fragment finds the value of the polynomial... How do I exactly show that? I don't understand what that would entail and my professor isn't exactly that helpful he says to prove it for all $n$, but I don't understand how to show that mathematically through programming. He says not just to give a particular example, but rather show it works for all polynomials.The whole question is this:It is required to find the value of the polynomial $$P(x)=\displaystyle\sum_{k=0}^n a_k x^k$$Show that the following pseudo-code fragment finds the value of the polynomial, given the coefficients $a_0,a_1,a_2,...a_n$ for a value of $x$.y = 0;i = n;while (i >= 0) {   y = a[i] + x * y;   i = i - 1;}
How to show that this algorithm for evaluating polynomials works?
algorithms;algorithm analysis;correctness proof