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anonymous

  • 5 years ago

is this series alternating ? sigma n=1 to infinity (-1)^n(2-1/n).

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  1. anonymous
    • 5 years ago
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    I don't think so, I think it's possible to have consecutive negative terms

  2. anonymous
    • 5 years ago
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    the answer is that its is but it doesnt satisfy the conditions

  3. anonymous
    • 5 years ago
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    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.

  4. anonymous
    • 5 years ago
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    If you plug in the n values, you're going to get imaginary numbers.. maybe every number that is real ends up alternating?

  5. anonymous
    • 5 years ago
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    Not that I found any.. lol

  6. anonymous
    • 5 years ago
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    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.

  7. anonymous
    • 5 years ago
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    Oh, then it's alternating for sure. (-1)^n would change the sign each time

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