(a) Show that if lim n a 2n = L and lim n a 2n+1 = L,...

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(a) Show that if lim_n→∞a_2n = L and lim_n→∞a_2n+1 =− L, then {an} is convergent and lim_n→∞a_n = L.

(b) If a₁ 1 and

find the first eight terms of the sequence {an}. Then use part (a) to show that lim_n→∞ an = √2 . This gives the continued fraction expansion

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Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

Authors: James Stewart, Daniel K. Clegg, Saleem Watson, Lothar Redlin

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Question Posted: May 20, 2021 06:18 AM

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(a) Show that if lim n a 2n = L and lim n a 2n+1 = L,...

Question:

1 Ar±1 =1 + 1+ an

Step by Step Answer:

a Let 0 Since there exists N 1 such that there exists N 2 such that If ...View the full answer

Calculus Early Transcendentals

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