Irrational sequence that converges to a rational limit

[cnwilson2010]

Hi. I found some rational sequences that converge to irrational limits, but am not having any luck going the other direction, i.e., an irrational sequence that converges to a rational limit. Any suggestions?

 

[micromass]

Can you find an irrational sequence that converges to 0? Something like \frac{1}{n} but with an irrational number in the numerator?

 

[cnwilson2010]

Thank you.

How about 1/n(2^(1/2))?

 

[micromass]

Thank you.

How about 1/n(2^(1/2))?

Yes, that sounds good!

 

[gb7nash]

You can also use a commonly known irrational number (e.g. pi or e) and do something similar.

 

[cnwilson2010]

Didn't want to be oddly transcendental or anything, so I was trying to stay away from those, but found out later they would have been fine. So thank you for that.