Hello. I'm having problem with these:

a). Prove that the Bisection algorithm gives a sequence that has the bound of error which converges linearly to zero.

b). The sequence $\displaystyle F_n$ described as $\displaystyle F_0$, $\displaystyle F_1$, and $\displaystyle F_{n+2}=F_n+F_{n+1}, n\geq0$, is called Fibonacci sequence and $\displaystyle x_n=\frac{F_{n+1}}{F_n}, \lim_{n\to\infty}{x_n}=x$ exists, prove that that limit is $\displaystyle x=\frac{(1+\sqrt5)}{2}$. (This number is called golden ratio)

Thank you for your time.