limits. How do I show that $$\lim_{k\to\infty} \frac{(-1)^k}{k}=0$$

Question

shubhamsrg · Answer

Do you know LH rule ?? Where you can differentiate the numerator and denominator.

richyw · Answer

sorry I keep messing up the latex and openstudy is so slow.

richyw · Answer

and yeah I know lh rule could be applied since $k\in\mathbb{R}$. But how does that help?

shubhamsrg · Answer

Okay since it is (-1) , LH rule won't be applied.

shubhamsrg · Answer

hmm, so, think like this :
(-1)^n , where n is any natural number, will always be equal to +1 or -1 right ?

richyw · Answer

agreed. and since $k\to\infty$ I can see that it's 0. just not sure how to show that in any sort of rigorous way.

richyw · Answer

I need to show it though to show that a series is convergent.

shubhamsrg · Answer

hmm, Am not too comfortable with that. 
@phi

phi · Answer

I thought the definition of a limit L  is that for any $ \epsilon >0$, there exists an integer N>0 such that $ | L - x_n| < \epsilon $ for all n>N

the alternating sign does not affect this definition, because you are only looking at the distance away from L. (0 in this case)