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Math Help - find the limit if it's converge

  1. #1
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    find the limit if it's converge

    2^n/(4^n+1)


    i know it's converge to 0, but I have trouble dealing with the n expontial, can someone tell me the general methof for finding the limits for a^n/(b^n + 1)
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  2. #2
    Super Member Random Variable's Avatar
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     \lim \frac{2^{n}}{1+4^{n}} =\lim \frac{\frac{2^{n}}{4^{n}}}{\frac{1}{4^{n}}+\frac{4  ^{n}}{4^{n}}}

     \lim \frac{\frac{1}{2^{n}}}{\frac{1}{4^{n}} + 1} = \frac{0}{0+1} = 0
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  3. #3
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    thanks, i have got another one, n^2/\sqrt{2n^4+1}

    how do I deal with the squre root?
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  4. #4
    Super Member Random Variable's Avatar
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    Quote Originally Posted by wopashui View Post
    thanks, i have got another one, n^2/\sqrt{2n^4+1}

    how do I deal with the squre root?
    Divide the numerator and the denominator by n^{2}. When you bring the  n^{2} inside of the radical it becomes  n^{4}
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  5. #5
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    Quote Originally Posted by Random Variable View Post
    Divide the numerator and the denominator by n^{2}. When you bring the  n^{2} inside of the radical it becomes  n^{4}


    hmm, I dun quite understand it, can you show me the steps please?
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