A)Every bounded sequence has a convergent subsequence. That sequence is a Cauchy sequence.

B)No. s_n=n.

1<= x <= n for sufficiently large n.2)

Suppose that x>1. Prove that Lim x^(1/n) = 1

Then,

1<=x^{1/n} <= n^{1/n}

Squeeze theorem.

Use famous fact that,

n^{1/n} --> 1