Use the integral test to determine if the following series converges or divergesoo1n In n2First, show that the conditions required for the integral test apply1d. Enter DNE or to0 (if appropriate) if the integral diverges. No decimal entries[A] Find the value ofallowedOO1daInr[B] Based on this, does the series converge?DivergesConverges

Question
Asked Nov 26, 2019
12 views
Use the integral test to determine if the following series converges or diverges
oo
1
n In n
2
First, show that the conditions required for the integral test apply
1
d. Enter DNE or to0 (if appropriate) if the integral diverges. No decimal entries
[A] Find the value of
allowed
OO
1
da
Inr
[B] Based on this, does the series converge?
Diverges
Converges
help_outline

Image Transcriptionclose

Use the integral test to determine if the following series converges or diverges oo 1 n In n 2 First, show that the conditions required for the integral test apply 1 d. Enter DNE or to0 (if appropriate) if the integral diverges. No decimal entries [A] Find the value of allowed OO 1 da Inr [B] Based on this, does the series converge? Diverges Converges

fullscreen
check_circle

Expert Answer

Step 1
help_outline

Image Transcriptionclose

(A) 1 The given series is - nlnn n=2 du Let u In x then dx 1 dxdu _ x If u In x then the lower limit becomes, ln(2) If u nx then the upper limit becomes, o

fullscreen
Step 2
help_outline

Image Transcriptionclose

1 -dr as follows Integrate the 2 xlnx 1 1 xdu Jin2 x(и) xnx 1n2 и -[n(x)n и ln 2 =In (Inx) (u-Inx) (undefined) =diverges

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Other