Originally Posted by

**chris_panda85** Given

x_(n+1) = x_n - f(x)/f'(x_n) **(1)**

x_(n+1) = { x_n + -f'(x_n) ± √[f'^2(x_n) - 2f(x_n)f"(y_n)] } / f''(y_n) **(2)**

n=1,2,...

(2) can be write as,

x_(n+1) = x_n + { [2f(x_n)f'(x_n)] / [2f'^2(x_n) - f''(y_n)f(x_n)] } **(3)**

f(x_n) = f'(r) [ e_n + c_2 (e_n)^2 + c_3 (e_n)^3 + ... ] (4)

f'(x_n) = f'(r) [ 1 + 2c_2 e_n + 3c_3 (e_n)^2 + 4c_4 (e_n)^3 + ...] **(5)**

From (1) and (2),

f(x_n) / f'(x_n) = e_n - c_2 (e_n)^2 + 2[ (c_2)^2 - c_3] (e_n)^3 + ... **(6)**

How do I get eqn (6) using (4) and (5)? Please ...

Thanks !!!

P/s: _ represent subscript while ^ represent superscript / power