1. If lim (s n – s)/(s n + s) = 0, prove that lim s n = s. 2. Mark each statement True or False. Justify each answer. (a) If (s n ) and (t n ) are convergent sequences with s n → s and t n → t, then...

1. If lim (s_n
– s)/(s_n
+ s) = 0, prove that lim s_n
= s.

2. Mark each statement True or False. Justify each answer.

(a) If (s_n) and (t_n) are convergent sequences with s_n
→ s and t_n
→ t, then

lim (s_n
+ t_n) = s + t and lim (s_nt_n) = st.

(b) If (s_n) converges to s and s_n
> 0 for all n ∈ N, then s > 0.

(c) The sequence (s_n) converges to s iff lim s_n
= s.

(d) lim s_n
= +
 iff lim (1/s_n) = 0.