2 +n 10 2n 3 (-1)" 75. an n(-1)" 76. а, — 2 + п 78. а, — п3 — Зп + 3 77. an= 3 -2ne " od babnod Le) bas 79. Find the limit of the sequence 2, V2/2, V2/2/2 80. A sequence {an} is given by a1 = /2, an+ 1 = V2 + an. (a) By induction or otherwise, show that {a,} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim, an exists. (b) Find lim,n->* an . 81. Show that the sequence defined by boe i 1 = 3- an+1 a11 аn is increasing and an < 3 for all n. Deduce that {ant is conver- gent and find its limit. 82. Show that the sequence defined by 1 a1 2 an+1 3 an satisfies 0< an 2 and is decreasing. Deduce that the sequence is convergent and find its limit. l

2 +n 10 2n 3 (-1)" 75. an n(-1)" 76. а, — 2 + п 78. а, — п3 — Зп + 3 77. an= 3 -2ne " od babnod Le) bas 79. Find the limit of the sequence 2, V2/2, V2/2/2 80. A sequence {an} is given by a1 = /2, an+ 1 = V2 + an. (a) By induction or otherwise, show that {a,} is increasing and bounded above by 3. Apply the Monotonic Sequence Theorem to show that lim, an exists. (b) Find lim,n->* an . 81. Show that the sequence defined by boe i 1 = 3- an+1 a11 аn is increasing and an < 3 for all n. Deduce that {ant is conver- gent and find its limit. 82. Show that the sequence defined by 1 a1 2 an+1 3 an satisfies 0< an 2 and is decreasing. Deduce that the sequence is convergent and find its limit. l

Name: Number 80 in attached image. 2 +n102n 3(-1)"75. an n(-1)"76. а, — 2 +п
Uploaded: 2024-03-20T06:46:03.000Z
Channel: Bartleby
Description: Number 80 in attached image. 2 +n102n 3(-1)"75. an n(-1)"76. а, — 2 +п78. а, — п3 — Зп + 377. an= 3 -2ne "od babnod Le) bas79. Find the limit of the sequence2, V2/2, V2/2/280. A sequence {an} is given by a1 = /2, an+ 1 = V2 + an.(a) By induction or o

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...

See similar textbooks

Similar questions

Show that the sequence is convergent and find it's limit
Suppose real sequences (sn) and (tn) are bounded (That is, that their ranges are bounded sets.)1. Show the sequence given by (sn + tn) is bounded2. For any real number α, show that the sequence (α⋅sn) is bounded
What are the first five terms of the sequence defined over the natural numbers with the explicit function rule? ax = 3x-1
Determine if the sequence {an}∞n=1 with an=4n^2/√ (4n4+6n2)−converges. If it converges write its limit.
A sequence is defined by tn=tn−1+3n and t1=1 Determine the fourth term in this sequence
Utilize series in order to determine the limit for:
A sequence is bounded if it is bounded above and below. Suppose that {an} is bounded and that {bn}---->0. Prove that {anbn}---->0
limit as n approaches infinity of (1-n)/(3n+5)
Suppose a1=5sin15,a2=25sin125,a3=125sin1125,a4=625sin1625,a5=3125sin13125,...a1=5sin⁡15,a2=25sin⁡125,a3=125sin⁡1125,a4=625sin⁡1625,a5=3125sin⁡13125,... a) Find an explicit formula for anan: . b) Determine whether the sequence is convergent or divergent: .(Enter "convergent" or "divergent" as appropriate.) c) If it converges, find limn→∞an=limn→∞an=
Suppose that (sn) and (tn) are sequences so that sn = tn except for finitely many values of n. Using the definition of limit, explain why if limn → ∞ sn = s, then also limn → ∞ tn = s.
Help me real analysis every Cauchy sequence in dicreate metric space
uppose that the sn satisfies both limn→∞ s2n = 3 and limn→∞ s2n+1 = 3. (That is, the sequence given by the even terms of sn and that given by the odd terms of sn both converge to 3.) Show that also limn→∞ sn = 3.ii. Give an example of a sequence where the sequences given by the even and by the odd terms both converge, but where the entire sequence does not converge.