9-5 Geometric Series

Objective

To define geometric series and find their sums

Image Long Description

You can write any whole number that has the same digit in every place as the sum of the terms of a geometric sequence. For example,

4444 = 4 ( 10 ) 0 + 4 ( 10 ) 1 + 4 ( 10 ) 2 + 4 ( 10 ) 3 4444 , equals 4 . open 10 close to the . plus 4 . open 10 close to the first . plus 4 . open 10 close squared . plus 4 . open 10 close cubed

You can write any rational number as an infinite repeating decimal. For example, 47 90 = 0.5222 … 47 over 90 , equals , 0.5222 , dot dot dot

Therefore, you can write any rational number as a number plus the sum of an infinite geometric sequence.

0.5222 … = 0.5 + 2 ( 0.1 ) 2 + 2 ( 0.1 ) 3 + 2 ( 0.1 ) 4 + … 0.5222 , dot dot dot equals 0.5 plus 2 . open 0.1 close squared . plus 2 . open 0.1 close cubed . plus 2 . open 0.1 close to the fourth . plus dot dot dot

Essential Understanding Just as with finite arithmetic series, you can find the sum of a finite geometric series using a formula. You need to know the first term, the number of terms, and the common ratio.

A geometric series is the sum of the terms of a geometric sequence.

Table of Contents