# Irrational sequence that converges to a rational limit

1. Jun 26, 2011

### 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?

2. Jun 26, 2011

### micromass

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

3. Jun 26, 2011

### cnwilson2010

Thank you.

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

4. Jun 26, 2011

### micromass

Staff Emeritus
Yes, that sounds good!

5. Jun 26, 2011

### gb7nash

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

6. Jun 28, 2011

### 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.

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