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Power series

  1. Dec 17, 2007 #1

    tony873004

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    1. The problem statement, all variables and given/known data
    My notes are missing a step. How do I get [tex]\frac{{x^{n + 1} }}{{\sqrt {n + 1} }}\frac{{\sqrt n }}{{x^n }} = \frac{{x\sqrt n }}{{\sqrt {n + 1} }}[/tex]


    2. Relevant equations
    I'm trying like this, but I don't seem to be arriving at the same step as the example:
    [tex]\frac{{x^{n + 1} }}{{\sqrt {n + 1} }}\frac{{\sqrt n }}{{x^n }} = \frac{{x^{n + 1} }}{{\sqrt {n\left( {1 + \frac{1}{n}} \right)} }}\frac{{\sqrt n }}{{x^n }} = \frac{{x^{n + 1} }}{{\sqrt n \sqrt {\left( {1 + \frac{1}{n}} \right)} }}\frac{{\sqrt n }}{{x^n }} = \frac{{x^{n + 1} }}{{\sqrt {\left( {1 + \frac{1}{n}} \right)} }}\frac{1}{{x^n }}[/tex]

    Thanks!
     
  2. jcsd
  3. Dec 17, 2007 #2

    tony873004

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    Never mind. I figured it out. x^(n+1)/x^n = x
     
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