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Find the limit of n(sqrt(n+1) - sqrt(n))^2

  1. Nov 18, 2007 #1
    1. The problem statement, all variables and given/known data

    Compute lim n-> infinity for xn = n(sqrt(n+1) - sqrt(n))^2

    2. Relevant equations

    non (as far as i know)

    3. The attempt at a solution

    i tried logging it, didnt get me very far though, i had logxn -> log infinty + 2 log sqrt infitity ?????????

    pretty stuck...
  2. jcsd
  3. Nov 18, 2007 #2


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    Homework Helper

    If I'm reading this right, the next thing to do would be to go ahead and multiply out the binomial square to get

    (n+1) - { 2 · sqrt(n+1) · sqrt (n) } + n

    = (2n + 1) - { 2 · sqrt(n+1) · sqrt (n) } .

    This is still an indeterminate difference, but we know what to do with those: multiply by 1 as the ratio of the conjugate factor,

    (2n + 1) + { 2 · sqrt(n+1) · sqrt (n) } ,

    divided by itself. The numerator simplifies considerably. Now multiply this ratio by the factor n that was originally in front of the squared term in x_n and apply what you know about the limit of a rational function as x approaches infinity.
  4. Nov 18, 2007 #3
    thanks :eek:)
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