Given the sequence defined by $a_{n+1} = \sqrt { 1 + a _ { n } }$ where $a_{1} = 1$. What is the limit of the sequence $\lim\limits_ { n \rightarrow \infty } a _ { n }$?

1. Using the process as described in problem 8-135, estimate the limit.

   Hint (a):

   $a_{5} =$
   $a_{6} =$
   $a_{7} =$
   $a_{8} =$
   $a_{9} =$
   $a_{10} =$
   

2. We can find the limit using algebra by solving the equation $L =\sqrt { 1 + L }$. Solve the equation to find the exact value of the limit.

   Hint (b):

   $L^{2} = 1 + L$
   $L^{2} − L − 1 = 0$
   Use the quadratic formula!