Infinite series problem

1. Oct 31, 2007

camilus

can anyone find a solution without using a calculator??

This is the problem:

Find the positive interger k for which $$\sum \limits_{n=4}^k {1 \over \sqrt{n} + \sqrt{n+1}} = 10$$

2. Oct 31, 2007

Count Iblis

Hint: Multiply numerator and denominator by sqrt(n) - sqrt(n+1)

3. Oct 31, 2007

leon1127

I suspect this will become something call telescoping series

4. Oct 31, 2007

sennyk

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. Oct 31, 2007

sennyk

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.

6. Oct 31, 2007

robert Ihnot

This is a very easy problem because it reduces to:

$$\sum \limits_{n=4}^k - \sqrt{n} + \sqrt{n+1}} = 10$$

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