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Math Help - evaluate limit

  1. #1
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    evaluate limit

    lim as n goes to infinity of square root of (n + square root of n+1) - square root n)


    does it equal 0
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by twilightstr View Post
    lim as n goes to infinity of square root of (n + square root of n+1) - square root n)


    does it equal 0
    try multiplying by the conjugate over itself
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    yes i have done so already.
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by twilightstr View Post
    yes i have done so already.
    ...and...? where are you getting stuck?

    just to make things a little less messy, note that if you make a substitution of t = \sqrt{n + 1} then your limit is the same as

    \lim_{t \to \infty} \frac t{\sqrt{t^2 + t - 1} + \sqrt{t^2 - 1}}

    now can you finish up?
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