How do you know when to use the nth term test?

If the individual terms of a series (in other words, the terms of the series’ underlying sequence) do not converge to zero, then the series must diverge. This is the nth term test for divergence. This is usually a very easy test to use.

When Can ratio test be used?

The ratio test states that: if L < 1 then the series converges absolutely; if L > 1 then the series is divergent; if L = 1 or the limit fails to exist, then the test is inconclusive, because there exist both convergent and divergent series that satisfy this case.

How do you use root test to determine if a series converges?

You use the root test to investigate the limit of the nth root of the nth term of your series. Like with the ratio test, if the limit is less than 1, the series converges; if it’s more than 1 (including infinity), the series diverges; and if the limit equals 1, you learn nothing.

Can you use the nth term test on alternating series?

The alternating series test can only tell you that an alternating series itself converges. The test says nothing about the positive-term series. Always check the nth term first because if it doesn’t converge to zero, you’re done — the alternating series and the positive series will both diverge.

When can you not use the divergence test?

Explanations (3) The simplest divergence test, called the Divergence Test, is used to determine whether the sum of a series diverges based on the series’s end-behavior. It cannot be used alone to determine wheter the sum of a series converges. Allow a series n that has infinitely many elements.

What does inconclusive mean when using the ratio or root test?

Divergence Test If limn→∞an=0, the test is inconclusive. This test cannot prove convergence of a series. If limn→∞an≠0, the series diverges.

What is nth root test?

The root test states that: if C < 1 then the series converges absolutely, if C = 1 and the limit approaches strictly from above then the series diverges, otherwise the test is inconclusive (the series may diverge, converge absolutely or converge conditionally).