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Let
a + ar + ar^2 + ar^3 + \dotsb
be an infinite geometric series. The sum of the series is $4.$ The sum of the cubes of all the terms is $10.$ Find the common ratio.

 Apr 11, 2024
 #1
avatar+33654 
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a+ar+ar2+...=a1r as long as r<1

 

a3+a3(r3)+a3(r3)2+...=a31r3  as long as r^3<1

 

So:  

a1r=4

and

a31r3=10

 

Can you take it from here?

 Apr 12, 2024

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