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Math Help - limit of a sequence/ analysis

  1. #1
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    limit of a sequence/ analysis

    Find the limit of the sequence with the general term given. a_{n}= (\sqrt{4-\frac{1}{n}}-2)n
    I believe it to be 0, but with small confidence.
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  2. #2
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    Re: limit of a sequence/ analysis

    \begin{align*}a_n & = \left(\sqrt{4-\dfrac{1}{n}}-2\right)n  \\ & = \dfrac{\left(4-\dfrac{1}{n}-4\right)n}{\sqrt{4-\dfrac{1}{n}}+2} \\ & = -\dfrac{1}{\sqrt{4-\dfrac{1}{n}}+2}\end{align*}

    As n \to \infty, \dfrac{1}{n} \to 0, so:

    \lim_{n \to \infty} a_n = -\dfrac{1}{\sqrt{4}+2} = -\dfrac{1}{4}
    Thanks from delgeezee
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