My Math Forum Question regarding uniform convergence

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 August 31st, 2010, 03:06 PM #1 Newbie   Joined: Aug 2010 Posts: 1 Thanks: 0 Question regarding uniform convergence Hello, I have a question as follows: Let f_n(x) = 1 + sin(x/n) + x/n Does the sequence *{f_n}n=1 to n=inf* converge pointwise on **[0,inf)**? If it does, what is the limit function? Does the sequence * converge uniformly on **? Does it converge uniformly on [0,1]? OK I've found that the sequence does indeed converge pointwise to f(x) = 1, and that it does not converge uniformly on **. I am however, struggling to work out if it converges uniformly on [0,1], Any help is appreciated, Thank you.
 September 1st, 2010, 02:37 PM #2 Global Moderator   Joined: May 2007 Posts: 6,641 Thanks: 625 Re: Question regarding uniform convergence The slowest convergence in the interval [0,1] is at x=1, so uniformity is shown by convergence at all x using the ? ? for x=1.

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