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Math Help - limit 1/sqrt(n)

  1. #1
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    limit 1/sqrt(n)

    We've been doing proving limits and sequences in class and have been given this as one of the practice questions.

    prove lim 1/sqrt(n)=0

    I've done |1/sqrt(n)-0|=1/sqrt(n)<E so N(E)=[1/E^2]+1 but that seems waaay to simple to the ones we did before, is there another way of doing this or that literally all I need to do?
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  2. #2
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    Re: limit 1/sqrt(n)

    Quote Originally Posted by carla1985 View Post
    We've been doing proving limits and sequences in class and have been given this as one of the practice questions.

    prove lim 1/sqrt(n)=0

    These proofs must begin with: Suppose that \epsilon>0 .

    Then we know that \epsilon^2>0 so \left( {\exists N \in \mathbb{N}} \right)\left[ {n \geqslant N \Rightarrow \frac{1}{n} < \epsilon ^2 } \right].

    Can you finish?
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  3. #3
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    Re: limit 1/sqrt(n)

    I'm a little confused by what definition that is. In class we had the definition of convergence to be:

    Let
    (an)n∈N be a sequence of real numbers. The sequence is called convergent to a ∈ R if for every ε > 0 there exists N =N(ε)∈N such that




    |an−a|<ε for all n≥N(ε).
    If (an)n∈N converges to a we call a the limit of (an)n∈N and we writelim an = a.
    n→∞




    so we start with an-a and solve for N(ε)
    Is that not the definition I need to prove this limit?
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  4. #4
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    Re: limit 1/sqrt(n)

    Carla1985
    there nothing wrong with your proof but follow Plato's method it is more rigorous...besides your sequence is a null sequence therefore a=0.
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