$4.$ Let the sequence $($an$)$ be defined so that a$1=1$ and an$+1=1/(2+$ a $2$ n $)$ for all n $1.$ a$.$ Show that, for all n $2,|$an$+1$ an$|12|$an $$ an$1|.$ b$.$ Deduce that $($an$)$ is Cauchy, hence convergent. What is the limit$?$