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February 21st, 2013, 05:45 AM  #1 
Newbie Joined: Feb 2013 Posts: 3 Thanks: 0  I need help to prove this limit??
Suppose p>1. Show/Prove that the limit as n goes to infinity of p^(1/n) = 1?????

February 21st, 2013, 06:54 AM  #2 
Senior Member Joined: Dec 2012 Posts: 372 Thanks: 2  Re: I need help to prove this limit??
Let the limit as n approaches infinity of p^(1/n) be x. Now take logarithms on both sides so that the limit as n approaches infinity of (1/n) log p equals log x. (You interswitch the limit and logarithm under the assumption that the limit does exist and is finite) Log p is a real finite positive number and the limit of (1/n) is 0 as n approaches infinity. Thus on the left you get 0 as your product. Log x equals 0 so that x equals 1. I hope all this makes sense to you when you interprete in math symbols on paper.

February 22nd, 2013, 05:47 AM  #3 
Newbie Joined: Feb 2013 Posts: 3 Thanks: 0  Re: I need help to prove this limit??
Thanks for the post this really helped!!!!


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