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Math Help - ratio test (series) urgent help

  1. #1
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    ratio test (series) urgent help

    hey i m not sure if i did the right if anyone can help
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  2. #2
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Legendsn3verdie View Post
    hey i m not sure if i did the right if anyone can help
    We need to fidn \lim\left|\frac{a_{n+1}}{a_n}\right|

    So now if a_{n}=5\cdot 5^{-n} then a_{n+1}={\color{red}5}\cdot 5^{-n+1}

    So your limit is \lim_{n\to\infty}\frac{5\cdot{5^{-n}}}{5\cdot{5^{-n+1}}}=\frac{1}{5}<1 thus convergent.
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  3. #3
    MHF Contributor chiph588@'s Avatar
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    Notice that your series is a geometric series.
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  4. #4
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    Quote Originally Posted by Mathstud28 View Post
    We need to fidn \lim\left|\frac{a_{n+1}}{a_n}\right|

    So now if a_{n}=5\cdot 5^{-n} then a_{n+1}={\color{red}5}\cdot 5^{-n+1}

    So your limit is \lim_{n\to\infty}\frac{5\cdot{5^{-n}}}{5\cdot{5^{-n+1}}}=\frac{1}{5}<1 thus convergent.
    whoa wut u did there mad me realize what i probably did wrong.. can u vouch if this is correct. i wrote my change in green:

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  5. #5
    MHF Contributor Mathstud28's Avatar
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    Quote Originally Posted by Legendsn3verdie View Post
    whoa wut u did there mad me realize what i probably did wrong.. can u vouch if this is correct. i wrote my change in green:

    Perfect
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