calculating infinity

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can someone tell me wich one of the two answers for these two limits is correct?

lim (-1)^(n) = 1 or -1
n-> +infinity
lim (-1)^(n) = 1 or -1
n-> -infinity

Thanks in advance.

  • calculating infinity -

    depends on n
    if n is even then the answer is +1
    if n is odd you get -1

    for:
    lim (-1)^(n) = 1 or -1
    n-> -infinity

    is really the same as
    lim 1/(-1)^(n)

    so the same reasoning as above applies

  • calculating infinity -

    1) I get it, except for
    lim (-1)^(n) = ?
    n-> +infinity
    is infinity even or odd?
    This is important because the result determines wheter the series that i was given is convergent or divergent.

    2) in another excercise I encauntered the following problem:

    is the following calculation with infinity allowed?:

    lim (ln (n))^(1/n) = (ln (inf.))^(0)=1
    n-> +inf.

    Again txs for answering.

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