Science:Infinite Series Module/Units/Unit 2/2.1 The Divergence Test/2.1.09 Final Thoughts on the Divergence Test

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Recall our Learning Objectives

In this lesson we covered only one topic:

  • the divergence test.

After reading this lesson and completing a suitable number of exercises, you should be able to, given an infinite series

  • apply the divergence to determine whether or not the infinite series diverges

Note that we cannot use the divergence test to determine whether or not an infinite series converges. If the divergence test fails to provide any information, we can only resort to other tests to establish convergence.

If the Limit Equals Zero, Do We Give Up?

Of course not! In the event that the limit equals zero, the divergence test yields no conclusion, and we can try any of the other tests we explore in the ISM. For example, in the next lesson we introduce the integral test, which can determine whether or not an infinite series converges or diverges provided our infinite series meets certain conditions.