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Evaluate the infinite geometric series: \(1-\frac{2}{7}+\frac{4}{49}-\frac{8}{343}+\dots\)

tertre  Apr 8, 2017
 #1
avatar+88775 
+1

We can split this into two series......

 

The first is 

 

 1 + 4/49 +16/2401 + 64/ 117649 ...........

 

And the sum of this series =         1 /  [ 1 - (2/7)^2 ] =   49/45

 

The second series can be written as

 

- [ 2/7, 8/343, 32/16807........]

 

And the sum of this series =  -  [  [2/7] / [1 - (2/7)^2 ] ]   =  -14/45

 

So.......the sum  is    (49/45) - (14/45)   =   35/45  =  7/9

 

 

 

cool cool cool

CPhill  Apr 8, 2017
 #2
avatar+2983 
0

Thanks so much!

tertre  Apr 8, 2017

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