My Math Forum I need help to prove this limit??

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 February 21st, 2013, 04:45 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, 05:54 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, 04:47 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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