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| a function whose domain is THE set of positive integers |
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| a sequence has a limit L if for and E>0 , the re exits a number N>0 such that whenever n>N, then [an-L] |
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| If a sequence {an} has a limit, the sequence is said to be convergent and an converges to that limit |
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| If the sequence is not convergent, it is divergent |
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Let an = f(n).
If lim f(x) = L and f is defined for every positive integer, then lim an = L |
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if {an} and [bn} are convergent sequences and c is a constant then:
lim c = c
lim (c an) = c lim an
lim (an +/- bn) = lim an +/- lim bn
lim (an * bn) = lim an * lim bn
lim (an/bn) = (lim an) / lim (bn) |
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| a sequence is said increasing if... |
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| a sequence is said to be decreasing if |
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