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Ratio test (convergent or divergent?)

  1. Apr 23, 2013 #1
    1. The problem statement, all variables and given/known data


    Ʃ n / 2^n
    n=1

    2. Relevant equations
    ratio test
    lim |a(n+1) / a(n)|
    n->∞

    3. The attempt at a solution

    I have the answer and the steps its just there's one part I am confused on,
    first I just apply n+1 to all my n terms, which gives me,


    Ʃ [(n+1)/2^(n+1)] / [n/2^n]
    n=1

    and if I multiply the a(n+1) part by the reciprocal of an, I don't understand how the terms 2^(n+1) and 2^n cancel each other out and leaves me with just a 2?
     
  2. jcsd
  3. Apr 23, 2013 #2

    joshmccraney

    User Avatar
    Gold Member

    consider rules of exponents (which boils down to multiplication). consider $$x*x=x^2$$ this is the same as $$x^1*x^1=x^{1+1}=x^2$$ thus it seems plausible that $$x^{n+1}=x^n*x^1$$ does this answer your question?
     
  4. Apr 23, 2013 #3

    Mark44

    Staff: Mentor

    No it doesn't. In the Ratio Test you look at the ratio an+1/an, NOT the sum of that ratio.
     
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