Expert: Sherman D. - 5/15/2005

Question
find the limit of the specified sequence or state that the limit doesn't exist.

1) 1/3, -1/9, 1/27, -1/81, 1/243,...
2) 1, -4, 9, -16, 25, -36,...";  

Answer
I don't think either one of these have a specific limit and here is why.

1.) You have both positive values and negative values.
I would use the equation (1/3)^x, both this only works for positive values not the negative values. You would have a limit of -(1/2) or (1/2), instead of just one limity, you would have either.

2.) Same reason. The equation would be x^2, but as said before, that only works for the positive side. If they were positive or negative instead of both, the limit would had been infinity.

In short, for you to have a limit, mostly 2 things must exist. 1.) Can't have positive and negative values. 2.) A Sequence must be consistent.

Since i haven't done sequences in awhile, 1 and 2 are mostly my opinions from experience. So don't just take my word for it.