What is the Integral Test for Convergence of an Infinite Series?

Answer 1

Integral Test

If #f# is a function such that #f(n)=a_n#, then
#sum_{n=1}^inftya_n# and #int_1^infty f(x)dx# converge or diverge together.

I hope that this was helpful.

Sign up to view the whole answer

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

Sign up with email
Answer 2

The Integral Test is a method used to determine the convergence or divergence of an infinite series. It states that if ( f(x) ) is a continuous, positive, and decreasing function for all ( x \geq 1 ), and if ( a_n = f(n) ) for all positive integers ( n ), then the series ( \sum_{n=1}^{\infty} a_n ) converges if and only if the improper integral ( \int_{1}^{\infty} f(x) , dx ) converges.

Sign up to view the whole answer

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

Sign up with email
Answer 3

The Integral Test states that if ( f(x) ) is a continuous, positive, and decreasing function for ( x \geq n_0 ) and ( a_n = f(n) ) for all ( n \geq n_0 ), then the series ( \sum_{n=n_0}^{\infty} a_n ) converges if and only if the improper integral ( \int_{n_0}^{\infty} f(x) , dx ) converges.

Sign up to view the whole answer

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

Sign up with email
Answer from HIX Tutor

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.

Not the question you need?

Drag image here or click to upload

Or press Ctrl + V to paste
Answer Background
HIX Tutor
Solve ANY homework problem with a smart AI
  • 98% accuracy study help
  • Covers math, physics, chemistry, biology, and more
  • Step-by-step, in-depth guides
  • Readily available 24/7