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What is the following value when expressed as a common fraction:

1/2 + 1/2^2 + 1/2^3 + ... + 1/2^8 + 1/2^9 + 1/2^10 + 1/2^11 + 1/2^12

 Jun 11, 2021
 #1
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Geometic sum

Common ratio =   1/2  = r

 

Sum

 

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

 

(1/2 ( 1 - (1/2)^(12))/(1 -1/2)   =  4095 / 4096

 

 

cool cool cool

 Jun 11, 2021
edited by CPhill  Jun 12, 2021

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