Suppose $| x | < 1$. Consider the infinite sequence $1 + x + x^{2} + x^{3} + …$.

1. Write an expression for the sum of the sequence.

   Hint (a):

   First find the common ratio, then use the formula for an infinite geometric series.

   Answer (a):

   $\frac{1}{1-x}$

2. What is the result when you use polynomial division to divide $1$by $1 − x$? Show the first five terms of the quotient.

   Hint (b):

   Look back at (a) and explore what that answer means.