Suppose {$\displaystyle a_n$} is defined by $\displaystyle a_{n+1}$= sqrt(2+$\displaystyle a_n$)
Show by induction that $\displaystyle a_n$<2.
Prove the limit.
$\displaystyle a_1$=sqrt(2) $\displaystyle a_2$=sqrt(2+(sqrt(2)))
Suppose {$\displaystyle a_n$} is defined by $\displaystyle a_{n+1}$= sqrt(2+$\displaystyle a_n$)
Show by induction that $\displaystyle a_n$<2.
Prove the limit.
$\displaystyle a_1$=sqrt(2) $\displaystyle a_2$=sqrt(2+(sqrt(2)))