Convergence of sequence

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September 21st 2009, 07:52 PM
roshanhero

Convergence of sequence

Prove that the sequence {1+1/n} converges to 1 as n tends to infinity. I used the limit of {1+1/n} as n tends to infinity and got the answer,but I want to prove it by the formal definition. How can we do that?
September 21st 2009, 08:12 PM
redsoxfan325

Quote:

Originally Posted by roshanhero

Prove that the sequence {1+1/n} converges to 1 as n tends to infinity. I used the limit of {1+1/n} as n tends to infinity and got the answer,but I want to prove it by the formal definition. How can we do that?

Pick $N=\frac{1}{\epsilon}$ . Thus, for $n>N$ ,

$\left|\left(\frac{1}{n}+1\right)-1\right|=\left|\frac{1}{n}\right|<\left|\frac{1}{1/\epsilon}\right|=\epsilon$
September 22nd 2009, 11:20 PM
roshanhero

How do we pick N=1/epsilon
September 23rd 2009, 05:33 AM
HallsofIvy

Do you understand what "pick" means?? You just say "if $N> 1/\epsilon$ then ..."

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