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# i need some help..

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Evaluate the infinite geometric series: $$1-\frac{2}{7}+\frac{4}{49}-\frac{8}{343}+\dots$$

Jun 29, 2020

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Leave the 1 out for now. Combine -2/7 and 4/49. This equals -10/49. Combine -4/49 and 16/2401. This equals -40/2401.

This forms an infinite geometric series with first term -10/49 and common ratio 4/49. (You can go on a few more times to see that it is in fact a geometric series).

The sum is $$\frac{-10/49}{1-\frac{4}{49}}=\frac{-2}{9}$$. We add this to our beginning 1 to find our final answer 1-2/9=7/9

Jun 29, 2020
edited by thelizzybeth  Jun 29, 2020
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Thank you!!

AnimalMaster  Jun 30, 2020
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The common ratio is simply r = -2/7, so the infinite sum is given by 1/(1 - (-2/7))  or 7/9

Jun 30, 2020
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Thank you!!

AnimalMaster  Jun 30, 2020