anonymous
  • anonymous
determine whether the sequence converges and if so find the limit.. -1to the power of n+1/n! (upper limit is +infinity and lower limit is n=1) help please :)
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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katieb
  • katieb
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anonymous
  • anonymous
Do you want to find |dw:1378815195437:dw|
anonymous
  • anonymous
|dw:1378815371328:dw|
anonymous
  • anonymous
It exactly is convergent. now wait a second ...

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anonymous
  • anonymous
it is diverge..so no need to find its limit..
anonymous
  • anonymous
my answer is right or not?
anonymous
  • anonymous
No, it is convergent ... suppose that \[\sum_{k=1}^{\infty} (-1)^{k -1} a _{k}\] such that; for every k, a_k>=0, a-k>=a-k+1, lime a-k = 0 when k tends to infinity. in this case the series \[\sum_{k=1}^{\infty} (-1)^{k -1} a _{k}\] is said to be convegent in this case a-k is 1/n! and surely tends to zero when n is chosen to be large at infinity. so the series is convergent.
anonymous
  • anonymous
but when I write the first 5 terms, i got this..1, -1/2, 1/6, -1/24 , 1/ 120 it as not tends to zero as it diverge..am i right?
anonymous
  • anonymous
What is your definition of convergence and divergence?
anonymous
  • anonymous
It is not possible to obtain the behavior of a sequence from adding a few number of its components.
anonymous
  • anonymous
Any questions? I have to go!
anonymous
  • anonymous
ok..never mind..i'll do it first..btw thanks ya..:)

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