Using Ratio Test to Decide Convergent/Divergent

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SUMMARY

The discussion centers on the application of the Ratio Test to determine the convergence of a series involving factorials. The initial attempt incorrectly calculated the limit, leading to confusion about the series' behavior. Upon correction, the proper ratio \(\frac{(n+2)!}{(n+3)!}=\frac{1}{n+3}\) was identified, resulting in a limit of 0, which confirms that the series converges absolutely. This highlights the importance of accurate ratio calculations in applying the Ratio Test.

PREREQUISITES
  • Understanding of the Ratio Test in calculus
  • Familiarity with factorial notation and operations
  • Knowledge of series convergence concepts
  • Basic limit evaluation techniques
NEXT STEPS
  • Review the Ratio Test for series convergence in calculus
  • Practice problems involving factorials and limits
  • Explore absolute convergence and its implications
  • Learn about other convergence tests, such as the Root Test
USEFUL FOR

Students studying calculus, particularly those focusing on series and convergence tests, as well as educators seeking to clarify the Ratio Test's application.

McAfee
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Homework Statement



MS5Nt.jpg


The Attempt at a Solution



7ctie.jpg


I got that the limit goes to infinity using the Ratio Test and that would mean B. But I'm not 100% percent sure. Just looking for some to verify my answer if I'm correct or not.
 
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McAfee said:

Homework Statement



MS5Nt.jpg


The Attempt at a Solution



I got that the limit goes to infinity using the Ratio Test and that would mean B. But I'm not 100% percent sure. Just looking for some to verify my answer if I'm correct or not.
Your limit is wrong, because your ratio is wrong.

\displaystyle\frac{(n+2)!}{(n+3)!}=\frac{1}{n+3}
 
SammyS said:
Your limit is wrong, because your ratio is wrong.

\displaystyle\frac{(n+2)!}{(n+3)!}=\frac{1}{n+3}

Wow. I haven't used factorials in a while and forgot how they were used. Now looking at the problem I get L=0. That tells me that the series converges absolutely.

Thanks a lot. There are so many things is math to remember when solving a problem.
 

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