1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
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...