1. Prove that if lim sup sn = + and k > 0, then lim sup (ksn) = + . 2. Let C be a nonempty subset of R. Prove that C is compact iff every sequence in C has a subsequence that converges to a point in...

1. Prove that if lim sup s_n
= +

and k > 0, then lim sup (ks_n) = +
.

2. Let C be a nonempty subset of R. Prove that C is compact iff every sequence in C has a subsequence that converges to a point in C.

3. Prove that every sequence has a monotone subsequence