Q. 10 - Calculus

Question

Briefly outline the advantages and disadvantages of using the two comparison tests to analyze the behavior of a series $\underset{k=1}{\overset{\infty }{\sum a_k}}$. 

Step-by-Step Solution

Answer

The properties of both tests is given below:

Step 1. Advantages and Disadvantages Comparison Test

Advantages: If you can find the right series to use for comparison, this test always gives an answer. 

Disadvantages: If the series does not easily compare to one of our “known” series, then you are out of luck. You also kind of have an intuition about whether or not the series you are testing is convergent or not so you can find the right series for comparison 

Step 2. Advantages and Disadvantages Limit Comparison Test

Advantages: This test is easier to apply than the comparison test. 

Disadvantages: It can also yield inconclusive results, when the limit doesn’t exist or when the cases in the statement of the test are not satisfied.