ANALYSIS of ALGORITHMS, Bulletin Board

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Help with, hopefully, a simple problem



I have 0 < p < q < 1 and n>=1 and integer with the function u(n) = n.log(q/p) / log( (1-p^n)/(1-q^n) )
 
I believe that u(n) is Big Theta( n / q^n )
 
Cn any offer a simple proof?
 
Thanking you all in advance
 
John Walker
Singapore

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