Write the example of each of given, or argue that such request is impossible.
i) The sequence which doesn't has 0 or 1 as term but has subsequences converging to each of the values.
ii) The monotone sequence which diverges but has the convergent subsequence.
iii) The sequence which has subsequences converging to every point in infinite set {1, 1/2, 1/3, 1/4, 1/5,...}.
iv) The Cauchy sequence which is monotone.
v) The monotone sequence which is not Cauchy
vi) The Cauchy sequence with the divergent subsequence
vii) The unbounded sequence having the subsequence which is Cauchy.