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Homework Help: A quick Limit

  1. Nov 24, 2007 #1
    1. The problem statement, all variables and given/known data

    Does xn converge (Sum from n=1 to infinity) of xn = 1/(n + SQRTn)

    2. Relevant equations

    Using comparision test

    3. The attempt at a solution

    I separted into fractions of 1/SQRTn - 1/(1 + SQRTn) and i know that both of these diverge since the power of n is less than one but am stuck as to whether is converges or diverges and how to prove it...
  2. jcsd
  3. Nov 24, 2007 #2
    [tex]\frac{1}{n+n}\leq \frac{1}{n+\sqrt{n}}[/tex]
  4. Nov 24, 2007 #3
    therefore xn divereges...?
  5. Nov 24, 2007 #4
    yeah that is right, since the harmonic series diverges, it also diverges when we multiply it by a constant.
  6. Nov 24, 2007 #5
    Non-zero constant.

    Not to offend you but that is what I like to call a "physics-type mistake".
  7. Nov 24, 2007 #6
    yeah that is what i actually meant, but thnx for pointing it out. and not am not offended in any way.
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