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The sum of the first terms n in the infinite geometric sequence {1/4, 1/8, 1/16, ..} is \(15/32\). Find n.

 Apr 6, 2022
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r = 1/2

 

Sum of first  n terms of an infinite series  = 

 

first term  [ 1  - (r)^n ] / [ 1 - r ] = 

 

(1/4) [ 1 - (1/2)^n ] / [ 1 -1/2 ]  =   15/32

 

(1/4) [ 1 - (1/2)^n ] / (1/2)   =15/32

 

(1/2) [ 1 - (1/2)^n ]  =  15/32

 

1 - (1/2)^n  =  30/32

 

1- (1/2)^n  =  15/ 16

 

(1/2)^n  = 1 -15/16

 

(1/2)^n = 1 /16

 

n = 4

 

cool cool cool

 Apr 6, 2022

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