# How do you use the integral test to determine the convergence or divergence of #Sigma 1/sqrtn# from #[1,oo)#?

The series

We have that:

Under these conditions the convergence of the series:

is equivalent to the convergence of the improper integral:

Evaluate the indefinite integral:

and we can see that the integral:

is not convergent.

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

To use the integral test to determine the convergence or divergence of the series Σ(1/√n) from n = 1 to infinity:

- Form the corresponding improper integral: ∫(1/√x) dx from x = 1 to infinity.
- Evaluate the integral.
- If the integral converges, then the series also converges. If the integral diverges, then the series also 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 Nth term test on the infinite series #sum_(n=1)^oo(n(n+2))/(n+3)^2# ?
- How do you determine if #a_n=1-1.1+1.11-1.111+1.1111-...# converge and find the sums when they exist?
- How do I use the Limit Comparison Test on the series #sum_(n=1)^oosin(1/n)# ?
- How do you find the positive values of p for which #Sigma lnn/n^p# from #[2,oo)# converges?
- Why does the integral test not apply to #Sigma (-1)^n/n# from #[1,oo)#?

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