Determine if the sequence is increasing, decreasing, not monotonic, bounded below, bounded aboveand/or bounded.3 — п(b) {(-3)"}-0(c) {sin (n)}4(a) {:n=41- 3nn=1

Please post the multiple questions separately. Here I answered 1st question as per our policy.

Answered: Determine if the sequence is…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Q1-A) Test the following sequence whether it is converging or diverging:- a. - [8m - 25/m] sin( 1 ) + ceath [msin( an sin()+cosh sim(!] MT
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.
The sequence {(-1)" cos(n²)}, has a convergent subsequence. True False
Mark each sequence {n} having the property that lim infan> inf{n: n € N}. n+∞0 U U 0 U Xn = = {cos(nπ/3)} (-1)"n n+1 Xn = In = 1 Xn= n 1 when n is odd, and n = 1+ - when n is even. n xn = (-1)" n n- (-1)"
Let n E N* and a, BE R. O a. The sequence a + is increasing %%3D O b. The sequence (-1)" -is decreasing The sequence p - is decreasing (4/3)" a 1. The sequence p is neither increasing nor decreasing (x4)"a e. The sequence a is increasing 彩 Type here to search AAc
6. Show that the sequence is not convergent. {sin n}=1\
If (xn) is an unbounded increasing sequence, then lim(x,) = O -1 - O 1 O +0

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

Determine if the sequence is increasing, decreasing, not monotonic, bounded below, bounded above and/or bounded. 3 – n 1ª (a) (b) {(-3)"}o (c) {sin (n)}=4 n=0 1- 3n ) n=1