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.

 

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