Homework Help

Find the sum of the infinite geometric series 8 + 4 + 2 + 1 +...if it exists

user profile pic

cstavro | eNoter

Posted September 19, 2013 at 11:58 PM via web

dislike 1 like

Find the sum of the infinite geometric series 8 + 4 + 2 + 1 +...if it exists

1 Answer | Add Yours

user profile pic

Mary Joy Ripalda | High School Teacher | (Level 3) Educator

Posted September 20, 2013 at 12:39 AM (Answer #1)

dislike 0 like

Before taking the sum, determine the common ratio between consecutive terms.

`r=4/8=1/2`

`r=2/4=1/2`

Hence, the common ratio is `1/2` .

Now that the common ratio is known, plug-in its value and the first term to the formula:

`S_(oo)=a_1/(1-r)`

`S_(oo)=8/(1-1/2)=8/(1/2)`

`S_(oo)=16`

Hence, the sum of the given infinite geometric series is 16. 

Join to answer this question

Join a community of thousands of dedicated teachers and students.

Join eNotes