Determine if the given sequence converges or diverges. If it converges, what is its limit?8∞n +1)In(6n) J5+ 3n3(a)2n2(d) {бп + 5n=0n=29n4 + 6n2{(Ъ)(e) an = In(6n³ – 4) – In(3n³ + 5n² – 7n + 8)6n4 – 5n2 + 9(-1)ª+7(2 – 8n) ln2 +9-n=6(c)(f) {cos(nT)}n=0n=2

As per the guidelines I am supposed to do the first question among multiple questions. So I am doing…

Answered: Determine if the given sequence…

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

6. Determine if n=1 -2n (n − 4) 6 43-2n (2 — n²) converges or diverges.
Find the sum of the series 1(-1)-1. A) e² (e-1) (e+1)³ B) n² by using the sum of the power series n²x-1. en-1 e² (e+1) (e-1)3 C) π² (n-1) (π+1)3 e³(e-1) (e+1)² D)- E) n²(n+1) (π-1)³
Q(A). Let {fn(x)}-1=3: be a sequence of functions + (x – 2)* S. n=1 defined over [2,3]. Show that: (a) fn(x) is meaurable and monotonic increasing for all n.
Lemma 4. Let {yn} be a positive solution of equation (1.1) with the corresponding sequence {z„} e So for n > N. Then: (i) (1– p)zn N; (ii) {zn¢n} is increasing for all n > N. Proof. Assume that {yn} is a positive solution of equation (1.1) with the corres- ponding sequence {zn} E So. Then z, is positive, Zn 2 yn, and Yn = Zn – Pnyo(n) 2 (1– p)zn, n>N> no, so (i) is proved. It easy to see that z, E So implies lim b,(Az,)“ = 0; n00 otherwise we would eventually have Az, > 0 contradicting z, E So. Similarly, lim a„A(b,(Azn)“) = 0. A summation of equation (1.1) then yields 9szs+1 Zn+1 LIs. s=n s=n s=n Summing once more, we obtain as t=s s=n or Azn 2-Zn+1Qn. Hence, A(zn&n) = PnAzn + Zn+1Ao, > Zn+1(A0n – OnQn) =0 since {0,} is a solution of the difference equation (Ao, – Qnºn) = 0. Therefore, {z,9n} is increasing and this completes the proof of the lemma.
2. Determine if the given sequence converges or diverges. If it converges, what is its limit? (e) a, = In(6n³ – 4) – In(3n³ + 5n² – 7n + 8) %3D (f) {cos(nx)}o
Which of the sequences {an} converge, andwhich diverge? Find the limit of each convergent sequence. an = (ln 3 - ln 2) + (ln 4 - ln 3) + (ln 5 - ln 4) +....+ (ln (n - 1) - ln (n - 2)) + (ln n - ln (n - 1))
1. Determine if each sequence converges or diverges. Find the limit of any convergent sequences. 4+n-3n² 4n²+1 (a) { (b) {ln(12n+2) - In(9+4n)} (2n-1)! n! (c) {. (d) cos(nπ) 2} n (e) {(1 + ²)"} (f) {n(√n² +1 − n)} 82n n!
(d) Let an 6n²+ n-1 ntn and bn = √n n+1' (i) Determine whether {an} is convergent or divergent. Explain briefly. (ii) Determine whether Σ(-1)n-¹b, is convergent or divergent. Explain briefly. n=1

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

Determine if the given sequence converges or diverges. If it converges, what is its limit? n+11 (d) In(6n) ) n=2 5+ 3n³ (a) 2n2 — бп + 5 n=0 9n4 + 6n2 (b) 1 ón4 – 5n² + 9 J (e) an = ln(6n³ – 4) – In(3n³ + 5n² – 7n + 8) n=6 (-1)"+7(2 – 8n) (c) n² + 9 (f) {cos(nr)}0 n=2 n=0