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.
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
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.
To determine the correct answers for the given limits, we need to understand the concept of oscillating sequences.
The sequence (-1)^n alternates between 1 and -1 as n varies. When n is an even number, (-1)^n equals 1, and when n is an odd number, (-1)^n equals -1.
Let's analyze the two given limits separately:
1. lim (-1)^n as n approaches positive infinity:
As n approaches positive infinity, the values of n become larger and larger. Since the sequence alternates between 1 and -1, it does not converge to a specific value. Therefore, the limit does not exist for this case.
2. lim (-1)^n as n approaches negative infinity:
As n approaches negative infinity, the values of n become more and more negative. Again, the sequence alternates between 1 and -1. So just like in the previous case, the limit does not exist for this case either.
Hence, both of the given limits do not exist.