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Math Help - Simplification through a radical

  1. #1
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    Simplification through a radical

    So I am trying to follow an example in my text which and I found a step that I cannot follow. The example is showing convergence or divergence using an alternating series test lim(n-> inf).

    The original problem is:

    (sum)[n=1] ( (-1)^(n+1) n^2 ) / (n^5 +5)^(1/2)

    The step I do not understand is from:

    n^2 / (n^5 +5)^(1/2)

    To:

     1 / (n + 5/(n^4) )^(1/2)

    I don't understand how it was simplified through the radical. Can anyone help me?
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  2. #2
    MHF Contributor red_dog's Avatar
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    \dfrac{n^2}{\sqrt{n^5+5}}=\dfrac{1}{\dfrac{\sqrt{n  ^5+5}}{n^2}}=\dfrac{1}{\sqrt{\dfrac{n^5+5}{n^4}}}
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  3. #3
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