MATH 009C Final Exam Study Guide

📗
MATH 09C: Study Guide
Type Study Guide

Class MATH 09C

Date @June 8, 2024 11:30 AM

Materials Practice Final.pdf

Quarter Spring



MATH 009C Study Guide
UCR MATH 009C Final Exam Study Guide (Spring 2024) with Professor Peter
Samuelson. Created based on the Final Practice Problems released on Canvas.


(Note: click on images to enlarge them)



Final Practice Problems




MATH 09C: Study Guide 1

, Series Tests
Geometric Series Test: Use for series of the form ∑ ar n  ​




converges if ∣r∣ < 1


Alternating Series Test: Use for series of the form ∑ (−1)n bn  ​ ​




converges if bn is ​




1. positive

2. decreasing

3. limn→∞ bn = 0
​ ​




Comparison Test: Compare with a known convergent or divergent series


Limit Comparison Test: Compare the limit of the ratio of the series terms with a
known convergent or divergent series



Ratio Test: Use for series with factorials or exponential terms
a
converges if limn→∞ ∣ an+1 ∣ < 1
​




​ ​




n ​




Root Test: Use for series with nth power terms

converges is limn→∞ ​
n
an < 1 ​




Divergence Test: Use to quickly check if the series diverges

if limn→∞ bn ​ ​ =
 0, the series diverges




MATH 09C: Study Guide 2

, Absolutely Convergent, Conditionally
Convergent, or Divergent
∞
Absolutely Convergent: A series ∑n=1 an converges absolutely if the series of
​ ​




∞
absolute values ∑n=1 ​ ∣an ∣converges
​




WHY? Because the terms an must be getting small enough for both the
​




absolute and non-absolute sums to converge




∞ ∞
Conditionally Convergent: A series ∑n=1 an converges conditionally if ∑n=1 an 
​ ​ ​ ​




∞
converges, but ∑n=1 ​ ∣an ∣does not converge (diverges)
​




MATH 09C: Study Guide 3