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Let \(P = 5^{1/5} \cdot 25^{1/25} \cdot 125^{1/125} \cdot 625^{1/625} \dotsm\) 

 

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

 May 26, 2022
 #1
avatar+33279 
+4

As follows:

You can now complete the problem.

 

(The £ sign in the 6'th line should be a 3 of course!!)

 May 26, 2022
edited by Alan  May 26, 2022

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