# 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?

You use the Cauchy test

take the limit

so it converge

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

According to the root test, the series converges.

I know that you have asked for the ratio test to test the convergence.

However, in this case, I would strongly recommend to do the root test instead.

You can transform your series as follows:

... take the limit...

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 prove that #sum_(n=1)^oo (n^(1/n)-1)# diverges?
- How do you find the nth term of the sequence #2,5,10,17,26,37,...#?
- how you solve: #lim_(n->oo)(2-sqrt2)(2-root(3)2)(2-root(4)2)...(2-root(n)2))# ?
- Using the integral test, how do you show whether #sum 1 / (n^2 + 1)# diverges or converges from n=2 to infinity?
- How do you test the alternating series #Sigma (-1)^n(2^(n-2)+1)/(2^(n+3)+5)# from n is #[0,oo)# for convergence?

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