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Math Help - Ratio Test, Convergence

  1. #1
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    Ratio Test, Convergence

    Determine if \sum_{j=0}^{\infty}\frac{j^2}{4^j} converges, using ratio test.

    Ok so i know that it is \lim_{j\to\infty}\mid\frac{\frac{(j+1)^2}{4^{j+1}}  }{\frac{j^2}{4^j}}\mid

    Which comes to \lim_{j\to\infty}\mid\frac{(j+1)^2}{4j^2}\mid

    Does that then become \lim_{j\to\infty}\mid\frac{1}{4}\mid + \lim_{j\to\infty}\mid\frac{2}{4j}\mid + \lim_{j\to\infty}\mid\frac{1}{4j^2}\mid = 1/4

    Therefore series converges as L<1?
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Ratio Test, Convergence

    The solution of the limit is correct. The serie converges because \frac{1}{4}<1.
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