====== Lecture 3 ======

First, we will get familiar with a few examples of convergent and non-convergent sequences. Then, we prove a few properties on convergent sequence, first, they are bounded; second, they can only converge to a single value. Then, we will prove some operations (+,-,/, etc) on convergent sequence. Finally, we prove a few useful examples of limit (Thm 9.7).  See also [[https://courses.wikinana.org/_media/math104-s21/note_jan_26_2021_2_.pdf | notes from previous semester]]

I will present a cool trick to find limit for a recursive defined sequence, e.g. $s_{n+1}=\sqrt{s_n+1}$, for whatever initial $s_1>0$. 

Discussion time: 9.2, 9.9(c), 9.15

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