13. Use the difference an+1 – an to show that the given sequence {a, } is strictly increasing or strictly decreasing. (5 + Зл — 2 An+l - an = 1 ; strictly decreasing (Зп — 2)(Зп + 2)" 2 strictly increasing (Зп — 2)(Зп + 1) (3n + 2)(3n – 1)' ; strictly decreasing 2 strictly decreasing (Зп — 2)(3л + 1) 2 strictly increasing (Зп + 2)(Зп — 1)

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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13.
Use the difference an+1 – an to show that the given sequence {a, } is strictly increasing or strictly decreasing.
(5
+
Зл — 2
An+l - an =
1
; strictly decreasing
(Зп — 2)(Зп + 2)"
2
strictly increasing
(Зп — 2)(Зп + 1)
(3n + 2)(3n – 1)'
; strictly decreasing
2
: strictly decreasing
(3n – 2)(3n + 1)'
2
; strictly increasing
(Зл + 2)(3п — 1)
15.
Write the first five terms of the sequence:
{vn² + 2n – n}"
Determine whether the sequence converges, and if so find its limit.
If the sequence diverges, indicate that using the checkbox.
NOTE: Enter exact answers.
a2 =
lim (Vn² + 2n – n) =
n+00
az =
The sequence diverges
a4 =
a5 =
Transcribed Image Text:13. Use the difference an+1 – an to show that the given sequence {a, } is strictly increasing or strictly decreasing. (5 + Зл — 2 An+l - an = 1 ; strictly decreasing (Зп — 2)(Зп + 2)" 2 strictly increasing (Зп — 2)(Зп + 1) (3n + 2)(3n – 1)' ; strictly decreasing 2 : strictly decreasing (3n – 2)(3n + 1)' 2 ; strictly increasing (Зл + 2)(3п — 1) 15. Write the first five terms of the sequence: {vn² + 2n – n}" Determine whether the sequence converges, and if so find its limit. If the sequence diverges, indicate that using the checkbox. NOTE: Enter exact answers. a2 = lim (Vn² + 2n – n) = n+00 az = The sequence diverges a4 = a5 =
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