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Math Help - help with limits

  1. #1
    Banned
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    help with limits

    hello

    stuck on these two

    a) limit of {[(-1)^n]/(n^3+1)^1/2}

    and

    b) limit of {3^n/(2^n_3^n}

    both for n->plus infinity
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  2. #2
    MHF Contributor red_dog's Avatar
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    1) \left|\frac{(-1)^n}{\sqrt{n^3+1}}\right|=\frac{1}{\sqrt{n^3+1}}\  to 0 as n\to\infty.

    Then \lim_{n\to\infty}\frac{(-1)^n}{\sqrt{n^3+1}}=0

    2) \lim_{n\to\infty}\frac{3^n}{2^n-3^n}=\lim_{n\to\infty}\frac{3^n}{3^n\left[\left(\frac{2}{3}\right)^n-1\right]}=\lim_{n\to\infty}\frac{1}{\left(\frac{2}{3}\righ  t)^n-1}=-1
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