February 20th, 2009, 08:51 AM  #1 
Newbie Joined: Dec 2008 Posts: 4 Thanks: 0  sequence, convergence
Suppose that is a sequence in . Define a sequence by , . Prove that if converges to then converges to .

February 20th, 2009, 09:01 PM  #2 
Senior Member Joined: Jul 2008 Posts: 144 Thanks: 0  Re: sequence, convergence
to apply Stolz theorem.

February 25th, 2009, 12:33 PM  #3 
Senior Member Joined: Nov 2007 Posts: 258 Thanks: 0  Re: sequence, convergence
Find . For , set . Let Then, for , and c/n goes to zero as n goes to infinity. The lower bound is proved similarily. 

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convergence, sequence 
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