Question

Give an example:
A sequence Sn of positive numbers with no upper bound which does not diverge to infinity.

Answer 1

Does this work:

(-1)^(2n)
____________
n

Answer 2

nope, (-1)^2n =1, the sequence has 1 is an upper bound

Answer 3

1/n ?

Answer 4

or is 1 still an upper bound in this case?

Answer 5

\(\dfrac{(-1)^{2n}}{n}=\dfrac{1}{n}\) has 1 is an upperbound