E= (-1)^(n)sin (1/n)/(ln(1+n))^(2) Converge or Diverge

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Homework Help Overview

The discussion revolves around the convergence or divergence of the series E= (-1)^(n)sin (1/n)/(ln(1+n))^(2). Participants are exploring the appropriate series tests to apply in this context.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are considering various tests for convergence, including the p-test and the integral test. There is a suggestion to note the behavior of sin(1/n) as n approaches infinity.

Discussion Status

The discussion is ongoing, with some participants offering hints and guidance on how to approach the problem. There is an emphasis on attempting a solution before seeking further assistance.

Contextual Notes

Participants are navigating the constraints of homework rules, which may limit the type of assistance they can receive. There is also a mention of needing to show work to facilitate further help.

Simkate
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Does the following series converge(absolutely or conditionally) or diverge?

E= (-1)^(n)sin (1/n)/(ln(1+n))^(2)

can anyone help me solve this or atleast tell me which series test to use?

thank u
 
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Hint: Note that sin(n-1) < n-1.
 
so do i jus use the p-test

don't i have to use the integral test making u=ln (n+1) ?
 
Rather than asking us what you should do at each step, why don't you try something and show us what you get? Post you working if you get stuck and then we can help you.
 

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