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--- math104-s22:notes:lecture_3 [2022/01/22 09:52]
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+++ math104-s22:notes:lecture_3 [2022/01/25 10:50] (current)
pzhou
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 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]]
-We will tackle exercises in Ross Sec9 in discussion time. You can prepare ahead of time.
+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
+{{:math104-s22:notes:pasted:20220125-105010.png}}
+{{:math104-s22:notes:pasted:20220125-105025.png}}
+{{:math104-s22:notes:pasted:20220125-105036.png}}

Lecture Notes