Which of the following converge quadratically and which converge linearly?
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.
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.
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..