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February 20th, 2009, 08:51 AM   #1
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sequence, convergence

Suppose that is a sequence in . Define a sequence by , . Prove that if converges to then converges to .
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February 20th, 2009, 09:01 PM   #2
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Re: sequence, convergence

to apply Stolz theorem.
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February 25th, 2009, 12:33 PM   #3
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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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