Question

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.

Answer 1

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

Answer 2

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.