Prove that

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- October 26th 2010, 02:22 AMNewtonianProve the limit of this sequence is 1
Prove that

- October 26th 2010, 12:39 PMzzzoak
As x goes to infinity the sum

may be evaluated

- October 26th 2010, 02:26 PMNewtonian
Sorry, I don't follow what you're trying to say. The sum may be approximated by the integral, but they're not equal, and the integral isn't equal to so I'm not quite sure what you're trying to show...could you explain a bit more please?

- October 26th 2010, 04:21 PMzzzoak
This sum is a Riemann sum of this integral.

For x going to infinity

- October 30th 2010, 09:19 AMNewtonian
OK I see what you're saying now. I think everything's fine as long as we can show that the approximation of the sum by the integral at the beginning is valid; that is, we need to show

as , where means as . I've thought about this for a while; is it just a standard kind of integration result or can you prove it?