# Finding an $n$ so the sequence $\left\{\frac{1}{n}\right\}_{n = 1}^\infty$ satisfies $|a_n| < 10^{-4}$

How to find $n$ so that $\left\{\frac{1}{n}\right\}_{n = 1}^\infty$ satisfies

$$|a_n| < 10^{-4}$$

I can't find this formula in my book anywhere. It seems like it would be very time consuming to just plug in numbers because I have way more to do than just this one. How do I do this before next Monday?

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I don´t understand your notation, would you mind explaining it? – chubakueno Jul 23 '13 at 21:50
It is what is provided, I don't entirely understand them either. – Paul the Pirate Jul 23 '13 at 21:52
If $a_n$ is supposed to mean $\frac1n$, then Peter Tamaroff has completely answered the question. If $a_n$ is supposed to mean something else, then you should say what it is supposed to mean. – Andreas Blass Jul 23 '13 at 21:52
Ok but just saying that he has completely answered it doesn't help me understand it. – Paul the Pirate Jul 23 '13 at 22:02

What about any $n$ such that $n>10^4$? Then $$\frac 1n <10^{-4}$$
it doesn't seem to work out when I plug it back in. Elaborate. – anon Jul 23 '13 at 22:08
What value did you get for $n$? What did you get when you plugged it into the function $f(x)=1/x$? (How are we supposed to pinpoint where you're going wrong when you won't show us your work? This sort of information is stuff you're supposed to put into your question in the first place.) – anon Jul 23 '13 at 22:11