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

Question:

(a) Show that if limn→∞a2n = L and limn→∞a2n+1 =− L, then {an} is convergent and limn→∞an = L.

(b) If a1 1 and

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

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus Early Transcendentals

ISBN: 9781337613927

9th Edition

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

Question Posted: