# Show that Newton's method applied to x^n - c = 0 produces the iterative scheme...

Show that Newton's method applied to $x^{n} - c = 0$ (where n and c are positive constants) produces the iterative scheme $x_{n+1} =\frac{1}{n}[(n-1)x_n + cx_n^{1-n}]$ for approximating $c^{\frac{1}{n}}$. We learned Newton's method, but we haven't applied it to "schemes" and my teacher told us to look at this problem tonight. Can someone explain, please! Thanks.