#### Problem 70E

70. (a) If $\left\{a_{n}\right\}$ is convergent, show that

$\lim _{n \rightarrow \infty} a_{n+1}=\lim _{n \rightarrow \infty} a_{n}$

(b) A sequence $\left\{a_{n}\right\}$ is defined by $a_{1}=1$ and $a_{n+1}=1 /\left(1+a_{n}\right)$ for $n \geqslant 1$. Assuming that $\left\{a_{n}\right\}$ is convergent, find its limit.