Limit ln(n-1/n+1) as n->infinity

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SUMMARY

The limit of ln((n-1)/(n+1)) as n approaches infinity is confirmed to be 0. The discussion highlights a common mistake involving the misinterpretation of the logarithmic expression, where the correct formulation is crucial for accurate computation. The user initially encountered issues with their HP50 calculator due to a formatting error, specifically using a decimal point incorrectly. The clarification provided by other forum members helped resolve the misunderstanding regarding the limit calculation.

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  • Understanding of logarithmic functions and limits
  • Familiarity with the properties of natural logarithms
  • Basic algebraic manipulation of fractions
  • Experience with graphing calculators, specifically HP50
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  • Study the properties of logarithmic limits in calculus
  • Learn about the behavior of functions as they approach infinity
  • Explore the use of graphing calculators for limit calculations
  • Review common pitfalls in algebraic expressions involving limits
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Students studying calculus, educators teaching logarithmic functions, and anyone looking to improve their understanding of limits in mathematical analysis.

AFinch
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Homework Statement


Hi! I need help confirming the limit of ln(n-1/n+1) as n->infinity.

If you multiply top and bottom of the quotient by 1/n you'd end up with ln(1) = 0, no? I must be missing something rather simple here because my hp50 won't even compute. Thanks!

Homework Statement

 
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AFinch said:

Homework Statement


Hi! I need help confirming the limit of ln(n-1/n+1) as n->infinity.

If you multiply top and bottom of the quotient by 1/n you'd end up with ln(1) = 0, no? I must be missing something rather simple here because my hp50 won't even compute. Thanks!

Homework Statement


Yes, you did it correctly. I'm not sure why the hp50 has problems.
 
Last edited:
Thank you! After getting your response I looked further into the problem with the hp and figured it out. I had a 1. instead of 1 (sans decimal), and it won't take a limit with the decimal because it's a "real" number. This was of much help.
 
AFinch said:

Homework Statement


Hi! I need help confirming the limit of ln(n-1/n+1) as n->infinity.

If you multiply top and bottom of the quotient by 1/n you'd end up with ln(1) = 0, no? I must be missing something rather simple here because my hp50 won't even compute. Thanks!

Homework Statement


You should realize that what you have written is ln[n + 1 - 1/n], which has no limit. Did you really mean ln[(n-1)/(n+1)]? If so, use brackets!

RGV
 
Yes ln[(x-1)/(x+1)] is what I actually meant, thanks for correcting my mistake.
 

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