Recently, we’ve worked on some problems about sequence converges and series converges. For certainty, there are some expressive sequences and series that I want to discuss.

We say that {an} is Cauchy  if an and am are arbitrarily close to each other provided n and m are sufficiently large.

This is how Professor Leung described in our pre-reading assignment. Cauchy sequence is a converge sequence which also has a converge subsequence. We can find that everywhere, we describing a diagram, composing a stock curve etc. Cauchy sequence applies in every part of our life especially in software and finance.

When considering a series, I will definitely link it with the annual saving rates of commercial bank. Longer the time you save your money in it, higher the saving rates you can get, just like a adding series.

Every time we playing sport like basketball, we could probably found out that after we throwing the basketball, flying trajectory was like a perfect curve function, which has a horizontal asymptote.