Find the general term of the sequence, starting with n = 1, determine whether the sequence converges, and if so find its limit. 6. 7 32 12' 42 22' 5² – 3² ’** 1 ' , sequence converges to n + 4 An (n + 2)? – n² n + 4 - , sequence converges to 4 a, = n2 – (n + 2)² ', sequence converges to n2 An = (n + 2)² 4' n + 4 An = (n + 2)? – n² sequence converges to 0. n + 4 an = ' , sequence does not converge. (n + 2)? – n2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 49E
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1, determine whether the sequence converges, and if so find its limit.
Find the general term of the sequence, starting with n =
7
6.
32
12' 4? – 2²' 5² – 3²’*
n + 4
An =
(n + 2)? – n²
', sequence converges to
n + 4
an =
sequence converges to
п? — (п + 2)?
n
an =
sequence converges to
(n + 2)? – n²
n + 4
, sequence converges to 0.
An
(n + 2)? – n?
n + 4
An
, sequence does not converge.
(n + 2)? – n²
Transcribed Image Text:1, determine whether the sequence converges, and if so find its limit. Find the general term of the sequence, starting with n = 7 6. 32 12' 4? – 2²' 5² – 3²’* n + 4 An = (n + 2)? – n² ', sequence converges to n + 4 an = sequence converges to п? — (п + 2)? n an = sequence converges to (n + 2)? – n² n + 4 , sequence converges to 0. An (n + 2)? – n? n + 4 An , sequence does not converge. (n + 2)? – n²
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