# What is the sum of the infinite geometric series 8 + 4 + 2 + 1 +... ?

##### 1 Answer

The common ratio is

etc ...

because the absolute value of

In our problem

Substitute

**The sum of this infinite geometric series is 16.**

Also, another formula you can use that is guaranteed to work **every time**, no matter what, is:

#S_n=a((r^n-1)/(r-1))#

All the variables work the same way as above, and "n" is the number of terms in the series. So, say you wanted to find the sum of the first **10 terms** and were to substitute everything in:

#S_10=8((0.5^10-1)/(0.5-1))#

#S_10=15.984375# Therefore the sum if the series is 15.98!

Hopefully this was helpful! You can use either formula, it's just a matter of preference; the second one is more reliable and accurate though! :)