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

[AFinch]

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

 

[Dick]

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.

 

[AFinch]

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.

 

[Ray Vickson]

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

 

[AFinch]

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