Mark each statement True or False. Justify each answer. (a) If lim s n = s and lim t n = t, then lim (s n t n ) = st. (b) If lim s n = + , then (s n ) is said to converge to + . (c) Given sequences (s...

Mark each statement True or False. Justify each answer.

(a) If lim s_n
= s and lim t_n
= t, then lim (s_nt_n) = st.

(b) If lim s_n
= +
, then (s_n) is said to converge to +
.

(c) Given sequences (s_n) and (t_n) with s_n
≤ t_n
for all n ∈ N, if lim s_n
= +
, then lim t_n
= +
.

(d) Suppose (s_n) is a sequence such that the sequence of ratios (s_n
+ 1/s_n) converges to L. If L <>_n
= 0.