State and explain in detail Hoare triple, pre-condition, post-condition and loop invariant and write the following program in C#:

The program reads a real number "x" and a sequence of non-zero integers c_1, c_2, ..., c_n to be ended by 0 (0 is just a marker not part of ci's) and prints the value of x^n+c_1*x^{n-1}+c_2*x^{n-2}+...+c_{n-1}*x+c_n.

N.B. The only operations allowed are + and * and should be proportional to n. No math functions and/or arrays are allowed!