(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);

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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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;
(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 sure
not to miss the cancellation magic.
Transcribed Image Text:(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; (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 sure not to miss the cancellation magic.
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