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Math Help - How to solve this limit

  1. #1
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    How to solve this limit

    How do you solve lim as n approaches infinity of (n^(1/n)+1)?
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  2. #2
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    Crna Gora
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    Re: How to solve this limit

    Hint :

    Set

    \ln A=\ln\left(n^{1/n}\right)

    and show :

    \lim_{n \to \infty}\ln A=0
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  3. #3
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    Re: How to solve this limit

    lim n→∞ (n^(1/n)+1) = lim n→∞ (n^(1/n)) +1

    lim n→∞ (n^(1/n)) is indeterminate, use L'Hopital's Rule
    First change the limit into e^(lim n→∞ ln(n^(1/n))) = e^(lim n→∞ (1/n)*ln(n))
    (1/n)*ln(n) = ∞/∞, take derivative of the numerator and the denominator
    e^(lim n→∞ (1/n)) = 1

    lim n→∞ (n^(1/n)+1) = 1+1 = 2
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