### Home > APCALC > Chapter 10 > Lesson 10.1.2 > Problem10-17

10-17.

For each of the series below, decide if there is a finite sum. If there is a finite sum, predict the sum. If there is not a finite sum, explain why.

1. $5 + 10 + 15 + 20 + …$

1. $0.1 + 0.01 + 0.001 + 0.0001 + …$

1. $4+\frac{4}{3}+\frac{4}{9}+\frac{4}{27}+...$

1. $2 − 2 + 2 − 2 + …$

For an infinite geometric series:

$S=\frac{a}{1-r}$

But $r$ must be _____.

The series in part (a) is arithmetic.
The other series are geometric. What is the value of $r$ in each case?