let n be a positive integer.It is give that ${(\sqrt{3}-1})^n=(-1)^{n-1}(a_{n}\sqrt{3}-b_{n})$ for some integers $a_{n}$ and $b_{n}$. a)show that $b_{n+1}=3a_{n}+b_{n}$ and $a_{n+1}=a_{n}+b_{n}$ b)prove,by induction that, $b_{n}\geq a_{n} \geq 2^{n-1}$ c)show that |$\sqrt{3}-\frac{b_{n}}{a_{n}}|\leq \frac{1}{2^{n-1}}$

Hence .find $\lim_{n\to\infty}\frac{a_{n}}{b_{n}}$

I don’t know how to do part (c),please help me.thx