+1(3) Define a sequence by $₁ = = 0, and Sn+1 = 8+¹ for all n € N.3(a) Prove by induction that 0 ≤ Sn ≤ 1 and s2 + 1 ≥ 3sn for all n.(b) Show that (sn) converges.(c) What is lim sn? Prove your answer using limit theorems.

Answered: Image /qna-images/answer/7624d215-940b-43c6-bb5e-b31ce11cecb1.jpg

Answered: (3) Define a sequence by $1 = 0, and…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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(3) Define a sequence by $1 = 0, and Sn+1 = +¹ for all n € N. 3 (a) Prove by induction that 0 ≤ Sn ≤ 1 and s2 + 1 ≥ 3sn for all n. (b) Show that (sn) converges. (c) What is lim sn? Prove your answer using limit theorems.