# Can the Alternating Series Test prove divergence?

By signing up, you agree to our Terms of Service and Privacy Policy

Yes, the Alternating Series Test can prove divergence. If the alternating series fails to meet the conditions of the test, specifically if the terms do not approach zero in absolute value or if the terms do not decrease in absolute value, then the series diverges.

By signing up, you agree to our Terms of Service and Privacy Policy

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

- How do you use the ratio test to test the convergence of the series #∑(5^k+k)/(k!+3)# from n=1 to infinity?
- How do you test for convergence for #sum ln(n)/n^2# for n=1 to infinity?
- If #a_n# converges and #lim_(n->oo) a_n -b_n=c#, where c is a constant, does #b_n# converge?
- Determine the convergence or divergence of the sequence an=nSin(1/n), and if its convergent, find its limit?
- How do you use the ratio test to test the convergence of the series #∑ ((4n+3)^n) / ((n+7)^(2n))# from n=1 to infinity?

- 98% accuracy study help
- Covers math, physics, chemistry, biology, and more
- Step-by-step, in-depth guides
- Readily available 24/7