Limit of n/(n+1)-n/(n+2) as n->Infinity: 0 or 1?

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Homework Help Overview

The discussion revolves around the limit of the expression n/(n+1) - n/(n+2) as n approaches infinity, and the apparent discrepancy when the expression is manipulated into a different form, specifically n/(n+1)/(n+2). Participants are exploring the implications of these limits in the context of calculus.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to understand why two different forms of the same expression yield different limits. There is a focus on the manipulation of the expression and the assumptions underlying these transformations.

Discussion Status

The discussion is ongoing, with some participants acknowledging mistakes in their reasoning and others questioning the validity of the manipulations. There is a recognition of the need for clarity regarding the equivalence of expressions and their limits.

Contextual Notes

Participants are grappling with the implications of manipulating mathematical expressions and the assumptions that lead to different limit results. There is a mention of potential errors in reasoning and the importance of maintaining equivalence in expressions.

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Take n/(n+1)-n/(n+2) as n->infinity results in the limit 0

But take the same equation convert it to n/(n+1)/(n+2) as n-> infinity results in the limit 1.

What is going on? The expression is the same yet you get two different limits. Something is wrong.
 
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pivoxa15 said:
Take n/(n+1)-n/(n+2) as n->infinity results in the limit 0

Correct.

But take the same equation convert it to n/(n+1)/(n+2) as n-> infinity results in the limit 1.

How? The expression is [n/(n+1)]/(n+2). Working from left to right, the limit reduces to (n/n)/(n+2) = 1/(n+2) = 0. (Very sloppy, but I can't do the tex now).
 
I see. I made a mistake in my OP.
 
pivoxa15 said:
Take n/(n+1)-n/(n+2) as n->infinity results in the limit 0

But take the same equation convert it to n/(n+1)/(n+2) as n-> infinity results in the limit 1.

What is going on? The expression is the same yet you get two different limits. Something is wrong.
?? And if you were to "convert" it into something else it is not equal to you would get yet a different answer! Garbage in, garbage out.
 
HallsofIvy said:
?? And if you were to "convert" it into something else it is not equal to you would get yet a different answer! Garbage in, garbage out.

The expressions are identically equal.
 

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