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

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Homework Help Overview

The discussion revolves around finding the limit of the expression ln((n-1)/(n+1)) as n approaches infinity. Participants are exploring the behavior of this logarithmic function in the context of limits.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to manipulate the expression by multiplying the numerator and denominator by 1/n to simplify the limit. Some participants question the correctness of the expression and suggest clarifying the notation used in the limit.

Discussion Status

Participants are actively engaging with the problem, with some providing corrections to the original expression and others confirming the approach taken. There is a recognition of potential misunderstandings regarding notation and limits.

Contextual Notes

There is a mention of a specific calculator issue related to the input format, which may have contributed to confusion in evaluating the limit. Additionally, the importance of proper notation in mathematical expressions is highlighted.

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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