13-5

This week we went over 13-5, which is sums of infinite series. You can never find an infinite sum of an arithmetic series,only a geometric series. You are only able to find a infinite series of a geometric series if |r|<1. The formula for finding the sum of a geometric series is s = (t1/r-1). To find where an infinite geometric series converges set |r|<1 and solve for x. To write a repating decimal, you use the formula as follows: what's repeating/place-1.

Example 1:

find the sum of the infinite geometric series

9-6+4-...

1. first, you have to plug into the formula.

s= 9/1-(-2/3)

2. now solve for s.

s= 9/(5/30

= 27/5

The sum of the infinite geometric series is 27/5.

Example 2:

express the following decimal as a rational number.

0.7777..

1. first, you have to plug into the formula

.7/1-.1

2. solve

= /9

the rational number is 7/9.