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Find the sum of the real values of x such that the infinite geometric series \(x+\frac{1}{2}x^3+\frac{1}{4}x^5+\frac{1}{8}x^7+\dots\) is equal to -12.

 Feb 21, 2019
 #1
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a1 = x     r = 1/2 x^2

 

Sn =  a1 (1-r^n)/(1-r) = a1/(1-r)         =    x /  ( 1 - 1/2x^2)  = -12

                                                                x = -12 + 6x^2

                                                                0 = 6x^2 -x - 12               x = 18/12     and     -16/12

                                                                                                          added together = 2/12 = 1/6           

 Feb 21, 2019

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