solution of recurrence relation I need help in solving recurrence relation:
$$x_{n+1} = \exp (-x_n) + 2; x_1 = 1$$
I suppose that I should, assuming the limit exists, solve: $a=e^{-a} + 2$. But how?

Let $f(x)=2+e^{-x}$. Our recurrence solves the equation $f(x)=x$ by Fixed Point Iteration. 
After the initial (poor) starting point $1$, the terms of the sequence are always above $2$.Because $|f'(x)|$ is quite a bit under $1$ in this region, the fixed point iteration converges. 
