# How do you determine the convergence or divergence of #sum_(n=1)^(oo) cosnpi#?

The series:

is indeterminate

We have:

so the series is not convergent.

If we look at the partial sums we have:

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

The series ( \sum_{n=1}^{\infty} \cos(n\pi) ) converges if the terms in the series approach zero as ( n ) approaches infinity. In this case, ( \cos(n\pi) ) alternates between -1 and 1 as ( n ) increases, so the series oscillates and does not converge. Therefore, the series 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.

- Using the integral test, how do you show whether #n/(n^2+1)# diverges or converges?
- What is the root test?
- How do you determine if the improper integral converges or diverges #int 5x^(2)e^(-x^(3))# from 1 to infinity?
- Evaluate the integral or show that it is divergent?
- How would I use the Comparison Test in calculus to solve the integral #(cos(4x) +3) / (3x^3 + 1)# from 1 to infinity?

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