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I'm currently studying limits because of my calculus class and i've wondered how for example wolfram alpha computes the limit of a sequence. Is it more a brute force way, or is there an efficient method to calculate/find them?

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I would guess, since most of the sequences we give are monotonic it would search for a greatest lower bound or least upper bound(if at all the sequence is convergent). – Dinesh Nov 9 '11 at 22:23

Different sequences require different methods. I'm sure alpha has a suite of methods available and it analyzes the sequence to see which (if any) of its methods applies. Not all that different from the way humans do it.

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Additionally, the most expedient route for a machine may not be the easiest route for a human, and vice-versa. – J. M. Nov 10 '11 at 0:20

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