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- Explain why if an converges, then limn→∞ an = limn→∞ an+1.C. Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ sn = s, then also limn → ∞ tn = s.Evaluate the limit limn→∞ nΣk=1 ( 1 / (1 +(√3/3 + (k−1)2√3/3n)2) 2√3/3n
- Show directly from definitions that if sn and tn are sequences so that limn→∞ sn = -8 and limn→∞ tn = ∞, then limn→∞ sn + tn = ∞.C. Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ sn = s, then also limn → ∞ tn = s. Explain this by just using definition of limit!ThanksMy questions are: •What is Xn? ・Why lim n→∞{f(Xn)} ≦lim n→∞{g(Xn)}?Any Thm about sequences?