Given $f ( x ) = \frac { 1 } { 1 - x }$:

1. Find the Maclaurin polynomial, $p_n (x)$, which approximates $f(x)$ near $x = 0$.

   Hint (a):

   The original function and first few derivatives are listed below. Do you see a pattern?

   More Help (a):

   Evaluate the original function and each of the derivatives at $x = 0$.

2. Write $p_n (x)$ using sigma notation.

   Hint (b):

   Simplify the terms in the equation given in Step 2 (a). Then write an expression for the general term. Use this in your summation.