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Topic: Limit Problem (Read 457 times) |
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ThudnBlunder
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towr
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Re: Limit Problem
« Reply #1 on: Jan 4th, 2007, 2:30am » |
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Taking an integration as approximation of the summation, I get
LN(sqrt(2) + 1)
Not entirely sure whether they are the same in the limit though.
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| « Last Edit: Jan 4th, 2007, 2:31am by towr » |
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Wikipedia, Google, Mathworld, Integer sequence DB
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Icarus
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Re: Limit Problem
« Reply #2 on: Jan 4th, 2007, 7:11pm » |
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If we pull a factor of 1/n out of all terms, what we have is (1/n)(f(1/n) + f(2/n) + f(3/n) + ... + f(n/n)), where f(x) = 1/sqrt(1+x2). This is a Cauchy sum for f for the interval [0,1]. Hence it's limit is the integral of f(x) over that interval, provided the integral exists. Since f(x) = d/dx(arcsinh x), the limit is as towr gave.
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| « Last Edit: Jan 4th, 2007, 7:12pm by Icarus » |
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