48. Consider the sequence described by $x_n = \frac{1}{1+n}$, $n = 0, 1, 2, \dots$
a. Find a suitable function $g(x)$ so that the sequence can be generated by means of repeated substitution in the form $x_{n+1} = g(x_n)$, $n = 0, 1, 2, \dots$
b. Determine the rate of convergence of the sequence to its limit.