Please show the work step by step . I am really struggling with this problem. 3. (a) Given that limr→∞ a2nL andlimr→0 a2n+1 =L, show that {an} isconvergent and lim,0 an= L. (b) Letaj = 1 and an+1 =1+1Write out the1+anfırst eight terms of {an}. Use part (a) to showthat limr→ An= V2. This gives thecontinued fraction expansionV2 = 1+12+2+...

Note:- In given problem you don't mention about x and also it is a known Theorem so assuming that…

3. (a) Given that lim, a2n = L and L, show that {an} is lim+00 a2n+1 = convergent and lim,→∞ an = L. (b) Let aj = 1 and an+1 1 and an+1 1+ 1 Write out the 1+an first eight terms of {an}. Use part (a) to show that lim,→00 an V2. This gives the continued fraction expansion 1 V2 = 1+ 1 2+ 2+...

3. (a) Given that lim, a2n = L and L, show that {an} is lim+00 a2n+1 = convergent and lim,→∞ an = L. (b) Let aj = 1 and an+1 1 and an+1 1+ 1 Write out the 1+an first eight terms of {an}. Use part (a) to show that lim,→00 an V2. This gives the continued fraction expansion 1 V2 = 1+ 1 2+ 2+...

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Please show the work step by step . I am really struggling with this problem.

3. (a) Given that limr→∞ a2n
L and
limr→0 a2n+1 =
L, show that {an} is
convergent and lim,0 an
= L. (b) Let
aj = 1 and an+1 =
1+
1
Write out the
1+an
fırst eight terms of {an}. Use part (a) to show
that limr→ An
= V2. This gives the
continued fraction expansion
V2 = 1+
1
2+
2+...

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