How do you test for convergence of #Sigma (3n-7)/(10n+9)# from #n=[0,oo)#?
By putting an limit in front.
By signing up, you agree to our Terms of Service and Privacy Policy
To test the convergence of the series Σ(3n-7)/(10n+9) from n=0 to infinity, you can use the limit comparison test. Let's compare it with the series Σ1/n.
First, find the limit of the ratio of the two series as n approaches infinity:
lim (3n-7)/(10n+9) / (1/n) = lim (3n-7)/(10n+9) * n = lim (3n^2 - 7n) / (10n + 9) = lim (3 - 7/n) / (10 + 9/n) = 3/10
Since the limit is a finite nonzero number, and 1/n is a p-series with p=1, which is known to converge, by the limit comparison test, the given series also converges.
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.
- What is the limit of # sinx /(x^2 - 4x)# as x approaches 0?
- Using the integral test, how do you show whether #sum1/(n^2 - 1)# diverges or converges from n=4 to infinity?
- How do you determine whether the infinite sequence #a_n=e^(1/n)# converges or diverges?
- How do you determine if the series the converges conditionally, absolutely or diverges given #Sigma ((-1)^(n))/((2n+1)!)# from #[1,oo)#?
- How do you show whether the improper integral #int (x^2)/(9+x^6) dx# converges or diverges from negative infinity to infinity?

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