van tigh as colguns le bus digust supe(a) Use Strategy D5 to show that the sequence (an) is null, wherethey((b)anDetermine whether the sequence2n! + n²2n + 2n²an1√n+1-1*=converges, naming any result or rule that you use. If the sequence doesconverge, then find its limit. Strategy D5 Null/non-null sequence.To show that the sequence (an) is null,rearrange the inequality |an| < ɛ to find aninteger N (generally depending on ɛ) suchthat an <ɛ, for all n > N.To show that the sequence (an) is not null,find one value of e > 0 for which there is nointeger N such that an < e for all n > N.E

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eigas ang us belges the bus digast laup (a) Use Strategy D5 to show that the sequence (an) is null, where xorem dgis ads to ano an = 1 √n+1-1 anoq

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.2: Arithmetic Sequences

Problem 64E

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Question

van tigh as colguns le bus digust supe
(a) Use Strategy D5 to show that the sequence (an) is null, where
they
(
(b)
an
Determine whether the sequence
2n! + n²
2n + 2n²
an
1
√n+1-1*
=
converges, naming any result or rule that you use. If the sequence does
converge, then find its limit.

Strategy D5 Null/non-null sequence
.To show that the sequence (an) is null,
rearrange the inequality |an| < ɛ to find an
integer N (generally depending on ɛ) such
that an <ɛ, for all n > N.
To show that the sequence (an) is not null,
find one value of e > 0 for which there is no
integer N such that an < e for all n > N.
E

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