### Home > A2C > Chapter 12 > Lesson 12.4.1 > Problem12-170

12-170.

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

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

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

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

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

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