richyw
  • richyw
limits. How do I show that \[\lim_{k\to\infty} \frac{(-1)^k}{k}=0\]
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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shubhamsrg
  • shubhamsrg
Do you know LH rule ?? Where you can differentiate the numerator and denominator.
richyw
  • richyw
sorry I keep messing up the latex and openstudy is so slow.
richyw
  • richyw
and yeah I know lh rule could be applied since \(k\in\mathbb{R}\). But how does that help?

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shubhamsrg
  • shubhamsrg
Okay since it is (-1) , LH rule won't be applied.
shubhamsrg
  • shubhamsrg
hmm, so, think like this : (-1)^n , where n is any natural number, will always be equal to +1 or -1 right ?
richyw
  • richyw
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
  • richyw
I need to show it though to show that a series is convergent.
shubhamsrg
  • shubhamsrg
hmm, Am not too comfortable with that. @phi
phi
  • phi
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)

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