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Find the sum of the real values of $x$ such that the infinite geometric series $x+\frac{1}{2}x^2+\frac{1}{4}x^3+\frac{1}{8}x^4+\dotsb$ is equal to $-12$.

 Aug 5, 2023
 #2
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I think it would be -12, use the infinite geometric series equation :

 

For this equation, it would be: x / ( 1 - 0.5x^2)

 

set this equation to equal -12, you will get 2 different x answers x = -4/3 and x = 3/2, however, one is eliminated 

 

x = - 1 (1/3 )

 

Credit : Melody 

 

Link : https://web2.0calc.com/questions/kevin-kangaroo-begins-hopping-on-a-number-line-at

 Aug 5, 2023

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