# Limit superior and inferior in a set that alternates between + and -

Let {Sn} = {1,1/2,-2/3,1/4,-4/5,1/6,-6/7......}

Find the set S of subsequential limits of Sn, the limit superior, and the limit inferior.

What Im having trouble understanding is how I find these things when the set goes in between negative and positive

• I set up two subsequences. The first one {1/2,1/4,1/6} converges to 1. The second one {1,-2/3,-6/7} converges to -1. Commented Nov 15, 2016 at 0:08
• What is the smallest negative value that occurs in your set? (To answer this, examine just the negative values.) Similarly: what is the largest positive value that occurs in your set? The sequences you constructed are useful, but not because of their limits, but because they help answer the questions I posed.
– avs
Commented Nov 15, 2016 at 0:08
• @avs yea I figured it out -1 and 1. Got messed up with the 1 in front! Commented Nov 15, 2016 at 0:09
• math.stackexchange.com/questions/1980205/…
– RJM
Commented Nov 15, 2016 at 0:11