(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Which of the following converge quadratically and which converge linearly?

a) 1/n^2

b) 1/2^(2n)

c) 1/sqrt(n)

d) 1/e^n

2. Relevant equations

All I've got in my lecture notes is: The sequence converges with order a if there exist constants a and C and integer N such that |x_(n+1) -x*| <= C|x_n -x*|^a, and n>=N.

3. The attempt at a solution

For a), I got the terms 1, 1/4, 1/9, etc, and concluded that it must converge linearly since I couldn't find a constant C such that x_(n+1) <= C(x_n). But I'm not sure if it's right, and I don't know how to explain it if it is right.

For b), I also had that it converges linearly, for the same reasons as above. Again, don't know how to explain it if it's right.

c) Same

d) Same

My answers seem really wrong because I don't think all of them converge linearly but I can't seem to find any constants C such that it works for quad convergence. I'm so confused..

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# Orders of convergence - how to prove that a sequence converges linearly/quadratically

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