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Find the limit of the given sequence

  1. May 14, 2015 #1
    • OP has been warned about posting a problem with no apparent effort
    1. The problem statement, all variables and given/known data
    Find the limit of the given sequence as n →∞

    2. Relevant equations
    (1+n^2)^(1/ln(n))

    3. The attempt at a solution
    Wolfram said the answer was e^2, though i cannot figure out why. Any help would be greatly appreciated.
     
  2. jcsd
  3. May 14, 2015 #2

    SammyS

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    What have you tried ?
     
  4. May 14, 2015 #3
    lim (1+n^2)^(e/eln(n))
    n→∞

    lim (1+n^2)^e
    n→∞
     
  5. May 14, 2015 #4

    SammyS

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    What the heck !

    How about e^(ln( the limit ))

    ln of the limit is limit of ln .

    What is ##\displaystyle\ \ln\left( (1+n^2)^{1/\ln(n)}\right) \ ?##
     
  6. May 14, 2015 #5

    Mark44

    Staff: Mentor

    Is the outer exponent above ##\frac e {eln(n)}##? If so, how did you go from and exponent of ##\frac e {eln(n)}## to an exponent of e? If you "cancel" the factors of e you would be left with an exponent of ##\frac 1 {ln(n)}##, which gets you right back to where you started.
     
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