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--- math121a-f23:august_30 [2023/08/26 22:04]
pzhou created
+++ math121a-f23:august_30 [2026/02/21 14:41] (current)
@@ Line 17: / Line 17: @@
 Series is like a discretized version of integral.
-===== exercises =====
+===== various tests for series convergence =====
+. what does absolute convergence mean for series?
+. the model convergent series
+  * $\sum_n 1/n^p$ for $p > 1$.
+  * $\sum_n 1/r^n$ for $r>1$
+. various tests
+  * comparison test, if $0<a_n < b_n$, and $\sum_n b_n$ converges, then $\sum_n a_n$ converges.
+  * ratio test
+  * root test
+===== exercises =====
+{{ :math121a-f23:boas._ex_ch1.pdf | some exercise from Boas's textbook}}, try 1,3, 4-8

Lecture Notes