Infinite series problem

  • Thread starter camilus
  • Start date
  • #1
146
0
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]
 

Answers and Replies

  • #2
1,838
7
Hint: Multiply numerator and denominator by sqrt(n) - sqrt(n+1)
 
  • #3
486
0
I suspect this will become something call telescoping series
 
  • #4
73
0
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?
 
  • #5
73
0
Rationalize for the computer

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?

If I rationalize the denominator first, it then gives me the correct answer. If anyone has any experiences with other CAS's, please share.
 
  • #6
1,056
0
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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