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 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©, 9.15