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(Solved) Question 2(16 marks) (a) Let k+2 k2 _ 3 ,k E N. Use Theorem 1.7 in the lecture notes to derive the limit of < xi > as k r 00. (Jag): (2...


need help with this two questions about limits and functions. thank you!Screen Shot 2017-04-28 at 15.06.32.pngScreen Shot 2017-04-28 at 15.07.57.png

Question 2(16 marks) (a) Let k+2
k2 _ 3 ,k E N.
Use Theorem 1.7 in the lecture notes to derive the limit of < xi > as k —r 00. (Jag): (2 marks)
(b) Is < xk > a bounded sequence? Briefly explain. (2 marks)
(e) According to Definition 1.15 in the lecture notes, what must you Show to prove that L is the limit of < x1; >, where L is your answer to (a) above. (2 marks) (d) Prove that
létzg —L| <: khvmz.
(6 marks) (13) Use the result reported in (d) to prove that < xk >—r L. Report all steps in the proof. No
marks will be awarded for an unsupported answer. (4 marks)

 


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