What do you do if the limit comparison test equals 0?

If the limit is zero, then the bottom terms are growing more quickly than the top terms. Thus, if the bottom series converges, the top series, which is growing more slowly, must also converge. If the limit is infinite, then the bottom series is growing more slowly, so if it diverges, the other series must also diverge.

When can the nth term test not be used?

The nth term test can confirm whether a series is divergent when the limit of the nth term is not equal to zero. But we’ve confirmed that lim n → ∞ f ( x ) = 0 , so, ∑ n = 1 ∞ f ( x ) is not divergent. Other than that, we can’t conclude whether the sequence is convergent or not.

Can limit of a sequence be zero?

So, the sequence converges for r=0 and in this case its limit is zero. Theorem 2 above now tells us that we must also have, limn→∞rn=0 lim n → ∞ ⁡ r n = 0 and so if −1

When can limit comparison test be used?

The limit comparison test shows that the original series is divergent. The limit comparison test does not apply because the limit in question does not exist. The comparison test can be used to show that the original series converges. The comparison test can be used to show that the original series diverges.

Why does the nth term test work?

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.

How does nth term mean?

The nth term is a formula that enables us to find any term in a sequence. The ‘n’ stands for the term number. We can make a sequence using the nth term by substituting different values for the term number(n).

Can you use nth term test for alternating series?

does not pass the first condition of the Alternating Series Test, then you can use the nth term test for divergence to conclude that the series actually diverges. Since the first hypothesis is not satisfied, the alternating series test does not apply.