anonymous
  • anonymous
is this series alternating ? sigma n=1 to infinity (-1)^n(2-1/n).
Mathematics
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anonymous
  • anonymous
is this series alternating ? sigma n=1 to infinity (-1)^n(2-1/n).
Mathematics
jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
I don't think so, I think it's possible to have consecutive negative terms
anonymous
  • anonymous
the answer is that its is but it doesnt satisfy the conditions
anonymous
  • anonymous
2-1/n is always positive for n>=1 so it is an alternating series. lim n->inf 2-1/n = 2 so it diverges by the alternating series test.

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anonymous
  • anonymous
If you plug in the n values, you're going to get imaginary numbers.. maybe every number that is real ends up alternating?
anonymous
  • anonymous
Not that I found any.. lol
anonymous
  • anonymous
i think he means (-1)^n * [2-1/n], and even if it were (-1)^(n*[2-1/n] then the terms approach (-1)^(2n) = 1, essentially equivalent to summing an infinite number of 1's, therefore, irrelevant of whether it exists in the complex plane, it diverges.
anonymous
  • anonymous
Oh, then it's alternating for sure. (-1)^n would change the sign each time

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