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Infinite series problem

  1. Oct 31, 2007 #1
    can anyone find a solution without using a calculator??

    This is the problem:

    Find the positive interger k for which [tex]\sum \limits_{n=4}^k {1 \over \sqrt{n} + \sqrt{n+1}} = 10[/tex]
  2. jcsd
  3. Oct 31, 2007 #2
    Hint: Multiply numerator and denominator by sqrt(n) - sqrt(n+1)
  4. Oct 31, 2007 #3
    I suspect this will become something call telescoping series
  5. Oct 31, 2007 #4

    Has anyone used Maxima as a CAS? I used Maxima to check my answer to this problem and it just gives me a huge sum of radicals. When I used its float command it gave me 9.9999999999996 as the sum for my answer. Are all of the CAS's this limited?
  6. Oct 31, 2007 #5
    Rationalize for the computer

    If I rationalize the denominator first, it then gives me the correct answer. If anyone has any experiences with other CAS's, please share.
  7. Oct 31, 2007 #6
    This is a very easy problem because it reduces to:

    [tex]\sum \limits_{n=4}^k - \sqrt{n} + \sqrt{n+1}} = 10[/tex]
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