Which Convergence Test to Use for ∑(k(k+2))/(k+3)^2 in Calculus?

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Homework Help Overview

The discussion revolves around the convergence of the series ∑(k(k+2))/(k+3)^2, a topic within calculus. Participants are exploring various convergence tests to determine the behavior of the series as k approaches infinity.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to apply the ratio test but expresses uncertainty about the formulation. Another participant questions the limit of the series as k approaches infinity and its implications. A hint is provided suggesting the use of the Divergence Test.

Discussion Status

The discussion is active, with participants exploring different tests for convergence. Some guidance has been offered regarding the Divergence Test, and there is acknowledgment of the original poster's initial overcomplication of the problem.

Contextual Notes

There is an indication of uncertainty regarding the appropriate convergence test to apply, and the original poster's initial approach may reflect a common challenge in identifying the simplest method for series convergence.

mickellowery
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Homework Statement



∑(k(k+2))/(k+3)^2 I honestly have no idea where to start with this I was going to try a ratio test but I wasn't sure if it would be (k+1)(k+3)/(k+4)2*(k+3)2/(k(k+2)

Homework Equations





3. The Attempt at a Solution
 
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What is the limit as k goes to infinity of

\frac{k(k+2)}{(k+3)^{2}} ?

What does this tell you?
 
Big Hint: Going off of what Dunkle said, use Divergence Test.
 
Yea I was trying my hardest to make this problem way harder than it needed to be. Thanks a lot for your help.
 

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