Calculus II, Section 3 Summary

Explain what is and Express each of the following as a rational number using geometric series     Determine if the following sum is finite   […]

Ratio Test

Example 1. Suppose we are given the series . Define We use the ratio test and write     Therefore we conclude the series is absolutely […]

Absolutely or Conditionally Convergence

Determine if series is convergent or divergent. If convergent, absolutely or conditionally?    

Comparison Test Problems

Apply either direct or limit comparison test. State your result in details.    

Alternating Series, Absolute & Conditional Convergence

Example 1. Suppose we are given the series Observe that this series is alternating and     and the sequence is non-increasing. Therefore, the given series […]

Comparison Test

Example 1. Suppose we are given the series Observe that since we have and therefore     We know the -series is convergent with Therefore by […]

Integral and Series Problems

Determine if the series is convergent or not, using integrals. (1)   (2)   (3)   (4)   (5)   (6)  

Integral and Series

Example 1. Suppose we are given . This associated function is continuous, positive and decreasing for . Therefore we know the improper integral (1)   and […]

Test for Divergence Problems

Determine if the test for divergence is applicable. Explain all the details. (1)   (2)   (3)   (4)   (5)   (6)