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The sum of the first \(n\) terms in the infinite geometric sequence \(\left\{\frac{1}{4},\frac{1}{8},\frac{1}{16},\dots \right\}\)  is \(\frac{255}{512}\) . Find  \(n\).

ant101  Dec 30, 2017
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avatar+81022 
+1

We have that

 

255/512  =  (1/4) [  1 - (1/2)^n  ]  /  [  1 - 1/2]    simplify

 

255/512 =  (1/2) [ 1 - (1/2)^n ]  

 

255 / 256 =  1 - (1/2)^n

 

(1/2)^n  =   1 -  255/256

 

(1/2)^n  =  1/256

 

(1/2)^n  =  (1/2)^8

 

So....n  = 8

 

 

cool cool cool

CPhill  Dec 30, 2017

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