For each of the following, prove or give a counterexample. (a) If (s n ) and (t n ) are divergent sequences, then (s n + t n ) diverges. (b) If (s n ) and (t n ) are divergent sequences, then (s n t n...

For each of the following, prove or give a counterexample.

(a) If (s_n) and (t_n) are divergent sequences, then (s_n
+ t_n) diverges.

(b) If (s_n) and (t_n) are divergent sequences, then (s_nt_n) diverges.

(c) If (s_n) and (s_n
+ t_n) are convergent sequences, then (t_n) converges.

(d) If (s_n) and (s_nt_n) are convergent sequences, then (t_n) converges