Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.sum_{n=1}^inftyfrac{1}{n+3}

postillan4

postillan4

Answered question

2021-03-08

Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series.
n=11n+3

Answer & Explanation

Latisha Oneil

Latisha Oneil

Skilled2021-03-09Added 100 answers

Integral Test:
If f(x) is continuous, positive and decreasing function on [k,] and f(n)=an then
If kf(x)dx is convergent then n=kan is also convergent.
If kf(x)dx is divergent then n=kan is also divergent.
Given that
n=11n+3
Using Integral test,
Here f(x)=an=1x+3
11x+3dx=[ln(n+3)]1
=ln()+ln4
=
Since integral 11x+3dx is divergent so using integral test n=11n+3 is also divergent.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?