12. Which of the choices below give(s) the best definition of convergence of a,? I. for any given e > 0,3 n(e) E R | a, - a|< e Vn 2n(e). II. for any given e > 0, 3 n(e) E R | a, – am 0,3 n(e) E R 3 a – e < a, < a + € V n2 n(e). A. I only B. I and III only С. П only D. I, II and III E None of the above choices A, B, C or D

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Let a, be a sequence of real numbers such that an+1 2 an, V n > 1 and a, → a as
n → 0o. Use this preamble to answer questions 11 and 12
h of these statomente
nce?
12. Which of the choices below give(s) the best definition of convergence of a,?
I. for any given e > 0,3 n(e) ER Ə | am – a |< e Vn 2 n(e).
II. for any given e > 0,3 n(e) E R | an – am |< e V n > n(e).
III. for any give e > 0,3 n(e) E R 9 a - e < a, < a +e Vn 2 n(e).
A. I only
B. I and III only
С. I only
D. I, II and III
E None of the above choices A, B,C or D
Transcribed Image Text:Let a, be a sequence of real numbers such that an+1 2 an, V n > 1 and a, → a as n → 0o. Use this preamble to answer questions 11 and 12 h of these statomente nce? 12. Which of the choices below give(s) the best definition of convergence of a,? I. for any given e > 0,3 n(e) ER Ə | am – a |< e Vn 2 n(e). II. for any given e > 0,3 n(e) E R | an – am |< e V n > n(e). III. for any give e > 0,3 n(e) E R 9 a - e < a, < a +e Vn 2 n(e). A. I only B. I and III only С. I only D. I, II and III E None of the above choices A, B,C or D
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