Ratio Test for Finding the 1(circled part) - Understanding the Process

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SUMMARY

The discussion centers on the Ratio Test for determining the convergence of series, specifically addressing the origin of the term "1" in the context of the test. Participants clarify that the "1" is not a mistake but rather a crucial component of the test's formulation. The conversation emphasizes the importance of understanding the differences in expressions used in the test, which can lead to confusion among students.

PREREQUISITES
  • Understanding of series convergence concepts
  • Familiarity with the Ratio Test methodology
  • Basic knowledge of mathematical notation and expressions
  • Experience with calculus, particularly limits
NEXT STEPS
  • Study the detailed derivation of the Ratio Test
  • Explore examples of series where the Ratio Test is applied
  • Learn about alternative convergence tests, such as the Root Test
  • Review common mistakes made when applying the Ratio Test
USEFUL FOR

Students of calculus, educators teaching series convergence, and anyone seeking to deepen their understanding of the Ratio Test in mathematical analysis.

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Homework Statement


where does the 1(circled part) come from ? is it a mistake ?

Homework Equations

The Attempt at a Solution

 

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Try look closer. There is a difference in the second expression apart from the 1.
 

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