show that sup S =1 where S =
proof:
1)
2) if v< 1 want to prove such that
(by using Archimedean property ) "this step true or not ??"
The first step is wrong: take odd n's and the limit is -1, and take now even n's and the limit is 1 ==> the limit doesn't exist.
And precisely this gives you the solution: take all the elements of the sequence with even n and show their limit is 1. Now just mention that for odd n's you have negative terms...
Tonio