SOLUTION: For which values of x will (-3x+5/2)+(-3x+5/2)²+(-3+5/2)³+.... be a converging series?

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Question 1176165: For which values of x will
(-3x+5/2)+(-3x+5/2)²+(-3+5/2)³+....
be a converging series?
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


A geometric series will converge whenever the common ratio is between -1 and 1.

-1+%3C+-3x%2B5%2F2+%3C+1

-1-5%2F2+%3C+-3x+%3C+1-5%2F2

-7%2F2+%3C+-3x+%3C+-3%2F2

7%2F6+%3E+x+%3E+1%2F2 (switch the direction of the inequality when dividing by a negative)

1%2F2+%3C+x+%3C+7%2F6

ANSWER: The series will converge for any values of x between 1/2 and 7/6.