I have a question from my assignment which requires me to prove that a sequence converges to 0 linearly, and another sequence that converges quadractically. I have no idea how to do this. The prof didn't talk much about it neither have the TA.(adsbygoogle = window.adsbygoogle || []).push({});

The textbook book just gives the following about convergence:

"A method that produces a sequence of {pn} of approximations that converge to a number p converges linearly if, for large values of n, a constant 0 < M < 1 exists with

|p - p(n+1)| <= M|p - pn|

The sequence converges quadractically if, for large values of n, a constant 0 < M exists with

|p - p(n+1)| <= M|p - pn|^2

"

The n, (n+1) are meant to be subscripts. Could someone prove an example sequence which converges linearly or quadractically? Or give me some tips on how to do so? Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# How to prove a sequence converges linearly or quadractically?

**Physics Forums | Science Articles, Homework Help, Discussion**