How do you find the positive values of p for which #Sigma n/(1+n^2)^p# from #[2,oo)# converges?
The series:
is convergent for
Consider the series:
Using this series for the limit comparison test:
By signing up, you agree to our Terms of Service and Privacy Policy
The series (\sum_{n=2}^{\infty} \frac{n}{(1+n^2)^p}) converges if (p > \frac{1}{2}).
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.
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 evaluate an infinite series?
- How do you find the nth term of the sequence #1/2, 1/4, 1/8, 1/16, ...#?
- How do you find #lim sin(2theta)/sin(5theta)# as #theta->0# using l'Hospital's Rule?
- What is the Direct Comparison Test for Convergence of an Infinite Series?
- How do you test the improper integral #int x^-0.9 dx# from #[0,1]# and evaluate if possible?

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