For a positive number c, consider the quadratic equation
[tex]x^{2} -x-c=0[/tex], [tex]x>0[/tex]
Define {[tex]x_n[/tex]} recursively by fixing [tex]x_1\ \textgreater \ 0[/tex] and then,
if n is natural number for which {[tex]x_n[/tex]} has been defined, defining
[tex]x_{n+1}=\sqrt{c+x_n}[/tex]
Please help me prove the sequence {[tex]x_n[/tex]} converges monotonically to the solution of the above equation.
