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= n, ∀n ∈ℕ. (Sn* Tn)1, but Tndiverges to +9) Suppose Sn≤Tn, ∀n ∈ℕand lim(Sn) = +∞. Given M∈ ℝ, there exist n≥N implies that Snfor n≥N, Tn≥Sn>M lim(Tn) = +Suppose Sn≤Tn, ∀n ∈ℕand lim(Tn) = -∞. Given M∈ ℝ, there exist n≥N implies that Tnfor n≥N, Tn≤Sn< M lim(Sn) = -12) Suppose Snis convergent, then there exist M1∈ ℝsuch that |Sn|<M1, ∀n ∈ℕLet M=| M1+|s||. Given 𝜀>0, there exist N such that n>N| Sn- S|<𝑀* Sn≤Sn2|Sn2- S2|= |Sn- S||Sn+ S|< | M1+|s||| Sn- S |<𝜀| Sn- S |< 𝑀(M)=𝜀Sn2approaches S2∞>M ∞<M ∞. 𝜀𝜀
18) Suppose a≤Sn∀n ∈ℕ, then a≤lim(Sn)=s -Suppose s<a. Then ∀𝜀>0, there exist N∈ℕsuch that n≥N| Sn- S |< Section 4.3 k k