Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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
    Maxima

    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]
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Infinite series problem
  1. Infinite series (Replies: 1)

  2. Infinite Series (Replies: 11)

  3. Infinite Series (Replies: 2)

Loading...