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Calculate the sum of the geometric series 1 - 1/5 + 1/5^2 - 1/5^3 + .... Express your answer as a common fraction.

 Apr 2, 2022
 #1
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This is a geometric series with first term = 1 and common ratio = -1/5.

 

Using the formula for an infinite geometric series with a common ration -1 < r < 1:

      Sum  =  1 / ( 1 - 1/5)  =  1 / (4/5)  =  5/4.  

 Apr 3, 2022
 #2
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Sum == 1 / [1 - ( - 1/5)] ==1 / [1 + 1/5] ==1 / [6/5] ==5/6 [geno3141 made a small typo]

 Apr 3, 2022

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