(2) Show that each of the following sequences (an) in R is convergent, and determinelimn- ann² +n +2.(i) an4n²+1(ii) an = √9n² + 2n+1-3n;(¹)-(¹-) (¹) (1 - (+1²)=(iii) an (¹-3).(n(iv)* an = n/b²", where b is a real number with b > 1.....Hints: For (ii), recall that a-b= (a²-b²)/(a+b) for all a, b e R+; for (iii), make surenot to miss the cancellation magic.

According to guidelines we can do only first three sub parts.. thank you A sequence is said to be…

Answered: (2) Show that each of the following…

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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(2) Show that each of the following sequences (an) in R is convergent, and determine limn- an: n² +n +2. (i) an 4n²+1 (ii) an = √9n² + 2n +1-3n; (iii) an = (¹-22) (1¹-32)..... (1 (n + 1)²);