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Math Help - Convergence of sequence

  1. #1
    Member roshanhero's Avatar
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    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?
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by roshanhero View Post
    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
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    Member roshanhero's Avatar
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    How do we pick N=1/epsilon
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    Do you understand what "pick" means?? You just say "if N> 1/\epsilon then ..."
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