How can I tell if a sequence converges?
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"Suppose that I don't have a formula for #g(x)# but I know that #g(1)
= 3# and #g'(x) = sqrt(x^2+15)# for all x. How do I use a linear approximation to estimate #g(0.9)# and #g(1.1)#?"
1 Answer
Nov 5, 2014
A sequence
A useful result is that, if the terms of the sequence get arbitrarily close as
Written in a more mathematical notation, a sequence is a Cauchy sequence if and only if:
where
I hope that this was helpful.
