Convergence Tests: Help Setting Up Problem & Deriving Limit

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SUMMARY

The discussion revolves around setting up convergence tests in calculus, specifically using the comparison test to derive limits. The user initially struggled to understand the problem setup but later clarified that they successfully identified the limit as (5^(0.6))/(15^6). Despite initially believing this to be incorrect, they ultimately resolved the issue independently. The conversation highlights the importance of understanding convergence tests in mathematical analysis.

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  • Understanding of calculus concepts, particularly limits and convergence tests.
  • Familiarity with the comparison test for series convergence.
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  • Study the comparison test in detail, focusing on its applications in series convergence.
  • Explore other convergence tests such as the ratio test and root test.
  • Practice deriving limits using various convergence tests in calculus.
  • Review common pitfalls in limit calculations to avoid errors in future problems.
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Students and educators in mathematics, particularly those studying calculus and series convergence, as well as anyone seeking to improve their problem-solving skills in mathematical analysis.

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Generally when I post, it's with a specific problem. However in this case, the issue I'm running into is that I don't even have the slightest idea of how to even setup the problem to attempt it.

Honestly, I can't seem to find this anywhere in my book and I'm not sure what's really being asked of me. Perhaps it's something simple, but I'm not even sure where to start.

Here's a screencap of what I'm being asked to do.
http://i8.photobucket.com/albums/a3/Bivouac/Picture3-2.png?t=1292024780

I'm not looking for solutions (though I won't complain if one comes around), but I would just like to know what's being asked of me, and how to I setup for this kind of problem.

Any help is appreciated.EDIT: I figured it out. Via the comparison test, everything works out. My only issue now is with the last problem in the set. So any help on that one would be very much appreciated.

Via the comparison test, I derived the two highest powers as the limit approached infinity. This came out to be:

(5^(0.6))/(15^6), however it says that I'm wrong in doing this. Perhaps I'm missing something or made a mistake somewhere in the problem.
 
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