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

[pivoxa15]

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.

 

[Curious3141]

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).

 

[pivoxa15]

I see. I made a mistake in my OP.

 

[HallsofIvy]

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.

 

[Curious3141]

?? 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.