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Find the sum of the first five terms in the geometric sequence \(\frac13,\frac19,\frac1{27},\dots\). Express your answer as a common fraction.

 Jan 5, 2021

Best Answer 

 #2
avatar+292 
+1

CPhill I got something different 

This is a finite geometric series with first term \(1/3\) and common ratio \(1/3\). There are five terms, so the sum of this series is \(\frac{\frac13\left(1-\left(\frac13\right)^5\right)}{1-\frac13} = \boxed{\frac{121}{243}} \).

 Jan 5, 2021
 #1
avatar+114361 
+1

Sum of a geometric series

 

S =  first term  (  1 -  common ratio ^n)   / ( 1  - common ratio)     where n =  the  number of terms we are  summing

 

The common ratio  is    (1/9) / (1/3)  =  3/9  = 1/3

 

So

 

S =   ( 1/3)  ( 1 - (1/3)^3 ) / ( 1 - 1/3)   =

 

(1/3)  ( 1 - 1/27) / ( 2/3)   =

 

(1/3) (3/2)  * ( 26/27 )   =   

 

(1/2) ( 26/27)  = 

 

26/54  =

 

13/27

 

 

 

cool cool cool

 Jan 5, 2021
 #2
avatar+292 
+1
Best Answer

CPhill I got something different 

This is a finite geometric series with first term \(1/3\) and common ratio \(1/3\). There are five terms, so the sum of this series is \(\frac{\frac13\left(1-\left(\frac13\right)^5\right)}{1-\frac13} = \boxed{\frac{121}{243}} \).

hihihi Jan 5, 2021
 #3
avatar+114361 
0

OOOPS!!!...misread the problem....I just did the first three terms....your answer is  correct  !!!

 

THX for the  correction  !!

 

cool cool cool

CPhill  Jan 5, 2021
 #4
avatar+292 
+2

This ok

 Jan 5, 2021

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