• :00Days
  • :00Hours
  • :00Mins
  • 00Seconds
A new era for learning is coming soonSign up for free
Log In Start studying!

Select your language

Suggested languages for you:
Answers without the blur. Sign up and see all textbooks for free! Illustration

Q. 36

Found in: Page 625


Book edition 1st
Author(s) Peter Kohn, Laura Taalman
Pages 1155 pages
ISBN 9781429241861

Answers without the blur.

Just sign up for free and you're in.


Short Answer

Use either the divergence test or the integral test to determine whether the series in Exercises 32–43 converge or diverge. Explain why the series meets the hypotheses of the test you select.

36. k=1kk2+3

The series is divergent.

See the step by step solution

Step by Step Solution

Step 1. Given information

We have been given the series k=1kk2+3

We have to determine whether the series converge or diverge.

Step 2. Determine whether the series converge or diverge.

Consider function fx=x3+x2

The function is continuous, decreasing, with positive terms.

All the conditions of integral test are fulfilled.

So, integral test is applicable.

Consider the integral localid="1649088344379" x=1fxdx=x=1x3+x2dx

localid="1649088398964" x=1fxdx=limkx=1kx3+x2dx=12limku=4k2+3duu (Put 3+x2=u2xdx=du)=12limkln u4k2+3=12limkln k2+3-ln 4=

The integral diverges.

So, the series is divergent.


Want to see more solutions like these?

Sign up for free to discover our expert answers
Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free
94% of StudySmarter users get better grades.