# How do you apply the ratio test to determine if #sum_(n=1)^oo (e^n(n!))/n^n# is convergent or divergent?

Please see the explanation.

Given: sum_(n=1)^oo (e^n(n!))/n^n

Now for the ratio test :

The ratio test is inconclusive.

However, if you do the limit test:

This shows that the sum diverges.

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

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 test the alternating series #Sigma ((-1)^(n+1)2^n)/(n!)# from n is #[0,oo)# for convergence?
- How do you find the 4-th partial sum of the infinite series #sum_(n=1)^oo(1/sqrt(n)-1/sqrt(n+1))# ?
- How do you test the series #Sigma 1/sqrt(n^3+4)# from n is #[0,oo)# for convergence?
- How do you know when to use L'hospital's rule twice?
- What should I put for using the integral test to determine whether the series is convergent or divergent?

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