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richyw
 2 years ago
limits. How do I show that \[\lim_{k\to\infty} \frac{(1)^k}{k}=0\]
richyw
 2 years ago
limits. How do I show that \[\lim_{k\to\infty} \frac{(1)^k}{k}=0\]

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shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0Do you know LH rule ?? Where you can differentiate the numerator and denominator.

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0sorry I keep messing up the latex and openstudy is so slow.

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0and yeah I know lh rule could be applied since \(k\in\mathbb{R}\). But how does that help?

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0Okay since it is (1) , LH rule won't be applied.

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0hmm, so, think like this : (1)^n , where n is any natural number, will always be equal to +1 or 1 right ?

richyw
 2 years ago
Best ResponseYou've already chosen the best response.0agreed. 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
 2 years ago
Best ResponseYou've already chosen the best response.0I need to show it though to show that a series is convergent.

shubhamsrg
 2 years ago
Best ResponseYou've already chosen the best response.0hmm, Am not too comfortable with that. @phi

phi
 2 years ago
Best ResponseYou've already chosen the best response.0I 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)
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