+0  
 
0
310
2
avatar+2615 

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

tertre  Apr 8, 2017
Sort: 

2+0 Answers

 #1
avatar+86649 
+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+2615 
0

Thanks so much!

tertre  Apr 8, 2017

10 Online Users

avatar

New Privacy Policy (May 2018)

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website. Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see cookie policy and privacy policy.