Please, conclude by the Bounded Convergence Theorem that the sequence

Ellie Castro 2022-04-30 Answered
Please, conclude by the Bounded Convergence Theorem that the sequence is convergent n
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Answers (1)

Trey Harrington
Answered 2022-05-01 Author has 10 answers

Let an=n
an=nen
anmin=n=0
For maximum
Put ddn[an]=0
ddn[nen]=0
enn(en)2=0
en(1n1)=0
en=0 n=1
n=1           en>0, not possible
anmax=1e
Thus, 0an1e
Given sequence is bounded
ddn[an]>0
en(1n)>0
1n>0
1>n
n<1
For n<1 sequence is decreasing, thus it is convergent

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