Lesson: Comparison Test for Series Mathematics
In this lesson, we will learn how to determine whether a series is convergent or divergent by comparing it to a series of known convergence using the comparison test.
Use the comparison test to decide whether the series is convergent or divergent.
Let . As , we see that , which suggests that is a divergent series. Verify this by finding the first integer where . You should check that this inequality remains true for all larger .
Consider the series .
Do the terms of this sequence tend to 0 as ?
Is the series convergent or divergent?