Find the general term of the sequence, starting withn = 1, determine whether the sequence converges, and if so find its limit. 3 4 5 2² – 1²° 3² – 2²' 4² – 32° - n + 2 1 an = (n + 1)? – n² , sequence converges to 27 n + 2 An , sequence converges to 0. (n + 1)? – n² n + 2 an = n? – (n + 1)² 1 , sequence converges to 2 n + 2 , sequence does not converge. an = (n + 1)? – n² 1 , sequence converges to a, = (n + 1)? – n² - I'N

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter7: Exponents And Exponential Functions
Section7.9: Geometric Sequences As Exponential Functions
Problem 26PPS
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Find the general term of the sequence, starting with n = 1, determine whether the sequence converges, and if so find its limit.
3
4
5
22 – 12' 32 – 2²' 4² – 3² *
n + 2
1
sequence converges to
an
%3D
(n + 1)² – n²
n + 2
an
sequence converges to 0.
(n + 1)? – n?
n + 2
an =
n? – (n + 1)?
1
-, sequence converges to
n + 2
An
, sequence does not converge.
(n + 1)² – n²
1
, sequence converges to
2°
an =
(n + 1)² – n²
Transcribed Image Text:Find the general term of the sequence, starting with n = 1, determine whether the sequence converges, and if so find its limit. 3 4 5 22 – 12' 32 – 2²' 4² – 3² * n + 2 1 sequence converges to an %3D (n + 1)² – n² n + 2 an sequence converges to 0. (n + 1)? – n? n + 2 an = n? – (n + 1)? 1 -, sequence converges to n + 2 An , sequence does not converge. (n + 1)² – n² 1 , sequence converges to 2° an = (n + 1)² – n²
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