Determine the convergence or divergence of the series. ∑n=1∞(1n2−1n3)

bobbie71G

bobbie71G

Answered question

2020-11-29

Determine the convergence or divergence of the series.
n=1(1n21n3)

Answer & Explanation

faldduE

faldduE

Skilled2020-11-30Added 109 answers

P-series test:
n=11np
If p>1 series is convergent
If p1 series is divergent
Series sum or difference rule:
If n=1an and n=1bn are both convergent then
n=1(an±bn)=n=1an±n=1bn
And sum of two convergent series is also convergent
Given that n=11np
Let n=1an=n=11n2 and n=1bn=n=11n3
Using p-series test both an and bn are convergent so using series sum or difference rule n=1(1n21n3)=n=11n2n=11n3
Since n=1an=1n2 and n=1bn=1n3 both are convergent. Hence n=1(1n21n3) is also convergent
Jeffrey Jordon

Jeffrey Jordon

Expert2021-12-27Added 2575 answers

Answer is given below (on video)

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?