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Math Help - calculating a limit

  1. #1
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    calculating a limit

    I need to calculate the limit of (1/3^(n+2)-1/5^(n+2))/(1/3^(n+1)-1/5^(n+1)) where n tends to infinity, i know the answer is 1/3 but I don't understand how you get that.
    Can anyone explain? I will be grateful for any help.
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  2. #2
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    Quote Originally Posted by joesmith View Post
    I need to calculate the limit of (1/3^(n+2)-1/5^(n+2))/(1/3^(n+1)-1/5^(n+1)) where n tends to infinity, i know the answer is 1/3 but I don't understand how you get that.
    Can anyone explain? I will be grateful for any help.
    Consider
    \displaystyle \frac{ 3^{-(n + 2)} - 5^{-(n + 2)}}{ 3^{-(n + 1)} - 5^{-(n + 1)}}

    \displaystyle = \frac{ \frac{1}{9} \cdot 3^{-n} - \frac{1}{25} \cdot 5^{-n}}{ \frac{1}{3} \cdot 3^{-n} - \frac{1}{5} \cdot 5^{-n}}

    Now multiply top and bottom by 3^n and see what happens.

    -Dan
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  3. #3
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    Thanks i've just figured it out
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