The recurrence relation to solve x = e-x using Newton-Raphson method is,
1
\({x_{n + 1}} = {e^{ - {x_n}}}\)
2
\({x_{n + 1}} = {x_n} - {e^{ - {x_n}}}\)
3
\({x_{n + 1}} = \frac{{(1+{x_n}){e^{ - {x_n}}}}}{{1 + {e^{ - {x_n}}}}}\)
4
\({x_{n + 1}} = \frac{{{x_n}{e^{ - {x_n}}}}}{{1 + {e^{ - {x_n}}}}}\)