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Let

P = 1/7 + 1/7^2 + 1/7^3 + ...

Then P can be expressed in the form a/b, where a and b are positive integers.  Find the smallest possible value of a + b?

 Dec 31, 2021
 #1
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You have listed 3 terms for P. But 2 terms only give you the smallest a and b:

 

P ==1/7 + 1/7^2 ==a/b ==8 / 49. So: a + b ==8 + 49 ==57

 

If have to evalute 3 terms, as you have it listed, you get: a==57  and  b==343

 Dec 31, 2021
 #2
avatar+22543 
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P is the sum of an infinite geometric series with initial term = 1/7 and ratio 1/7.

Using the formula for the sum:  sum  =  (1/7) / ( 1 - 1/7 ), you can get the sum and the answer to the question.

 Jan 1, 2022

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