Can the LCT be Used Without Showing the Comparison Test Will Not Work?

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Homework Statement


I was just wondering that when applying a comparison test or a limit comparison test, do i have to show that a comparison test does not work in order to use a LCT? Also, if i directly use LCT, will i get the same answer as in the regular comparison test?
Thanks.

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The Attempt at a Solution

 
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You do not have to first show that a comparison test will not work. If both tests are applicable then your result should be the same.

Convergence is independent of the test you use.
 

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