1. The problem statement, all variables and given/known data
This problem is a part of a set of problems, I've solved all of them and this problem remains
1. If f(x) is a non-zero polynomial of degree d, show that f(x) - f(x-1) is a polynomial of degree d - 1. (For the purposes of this result, it is convenient to define the degree of the zero polynomial to be -1.)
2.If f(x) = g(x) + h(x), show that f(x) - f(x-1) = g(x) - g(x-1) + h(x) - h(x-1)
3. Use the binomial theorem to calculate x^(k+1)/(k+1) - (x-1)^(k+1)/(k+1)
(Answer is: x^k - (kx^(k-1)/2) + (kC2)x^(k-2)/3 - ...... - kx^2/2 + x - 1/(k+1))
4. Suppose that for all i <= k one knows a polynomial f_i such that f_i(x) - f_i(x-1) = x^i . The last problem gave us fi for i = 0, 1, 2, 3, and 4. Combine your work on this problem in order to show you how to calculate . fk+1
I have solved the first 3 problems but I have no idea about how to solve the fourth one whatsoever, it is so confusing
