- #1

- 146

- 0

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]

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- Thread starter camilus
- Start date

- #1

- 146

- 0

This is the problem:

Find the positive interger

- #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

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

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

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

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