finding the value of a series of sum of square roots

HI,
I am attaching a maths problem, if anyone can help me solve this it would be great.
Thanks
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Commented:
The first term of the problem is the Basel Problem (which you can Google) and involves pi.
Since this question is academic in nature, I assume you are wanting guidance toward a solution more that just an answer?

What do you have so far? Do you understand the Basel Problem parts?
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Commented:
Is this a homework problem?  If so, what is particular problem you are studying?
Do you know what the p and q notation refers to?

Have you tried looking at the the first few (or few thousand) terms with Excel?
Are you interested in finding upper and lower bounds?
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Author Commented:
Hi,
I will try to look at Basels problem and see if similar approach works.
Couldnt work on this due to busy schedule.. will try it sometime soon
No this is not an homework problem just some math problem i found somewhere which i wanted to solve. p and q are not known.
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Commented:
P=1999 Q=2000
In the explanation below, I use the caret("^") to represent the exponent and state the square root as I don't have any graphics capability.
If you were to end the series at the point you show the + ... +
the value of 1/1^2 = 1, the value of 1/2^2 = .25, adding those to 1 = 2.25 and the square root of that is 1.5
next the value of 1/2^2 = .25, the value of 1/3^2 = .11111111, adding those to 1 = 1.3611111111 and the square root that = 1.1666666666
when added to the previous sum is 2.6666666666 which is the equivalent of 2 + (2/3). If you carry out for the next set of squares is 3.75 or 3 + (3/4), the next set  is 4 + (4/5) = 4.8, and so on. The answer for 1999 and 2000 is 1999.9995
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