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Math Help - Analysis help!

  1. #1
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    Analysis help!

    I need to prove this result, and although I can see that it is true, I cannot see how to prove it mathematically..rather than just putting in numbers!

    sqrt(n+1) - sqrt(n) tends to 0
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  2. #2
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    Quote Originally Posted by reeha View Post
    I need to prove this result, and although I can see that it is true, I cannot see how to prove it mathematically..rather than just putting in numbers!

    sqrt(n+1) - sqrt(n) tends to 0
    It depends on how rigorous a proof you require .... A simple approach is to multiply the expression by \sqrt{n + 1} + \sqrt{n} and simplify. You get \frac{1}{\sqrt{n + 1} + \sqrt{n}} and the limiting value is 'obvious' (you could use the sandwich/pinching/squeeze theorem).
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  3. #3
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    Oh ok I see,
    That seems to work out very simply, the question says 'give a careful justifcation' so I think that using the squeeze rule as you suggested should be ok! Thank you!
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