Convergence of {n/(n^2+1)}: Is it Possible?

[mmilton]

Homework Statement

Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit?

Homework Equations

The Attempt at a Solution

I believe it does converge because the higher power is in the denominator, so thus, it's limit is 0.

Any help or hints on if I'm headed in the right direction would be very much appreciated!

Thank you in advance.

 

[stony]

You are right, using the rules you've learned about infinity limits will get us ((1/n)/(1+(1/n^2))) and the limit of that as n approaches infinity is 0.

 

[SammyS]

Homework Statement

Is the sequence {n/(n^2+1)} convergent, and if so, what is it's limit?

Homework Equations

The Attempt at a Solution

I believe it does converge because the higher power is in the denominator, so thus, it's limit is 0.

Any help or hints on if I'm headed in the right direction would be very much appreciated!

Thank you in advance.

Multiply the numerator & denominator by 1/n .

 

[Whovian]

If you're talking about the SEQUENCE, then it converges. Use a useful little rule known as L'Hôpital.

If you're talking about the SERIES, use the Ratio or Integral tests. It diverges.