Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Problem 11.2.22. The nth Term Test Show that if an converges then lim an = 0. %3D n→∞

Problem 11.2.22. The nth Term Test Show that if an converges then lim an = 0. %3D n→∞

Advanced Engineering Mathematics
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
icon
Related questions
Question
100%

Real math analysis, I need help with problem 11.2.22.

thank you so much.

Theorem 11.2.15. Cauchy sequences converge Suppose (sn) is a Cauchy sequence of real numbers. There exists a real number s such that limn→∞ Sn = s. Sketch of Proof. We know that (sn) is bounded, so by the Bolzano-Weierstrass Theorem, it has a convergent subsequence (Snk) converging to some real number s. We have sn – s = |Sn – Snp + Snk s| < |Sn – Sni|+|Snk 8|. If we choose n and ng large enough, we should be able to make each term arbitrarily small.
Transcribed Image Text:Theorem 11.2.15. Cauchy sequences converge Suppose (sn) is a Cauchy sequence of real numbers. There exists a real number s such that limn→∞ Sn = s. Sketch of Proof. We know that (sn) is bounded, so by the Bolzano-Weierstrass Theorem, it has a convergent subsequence (Snk) converging to some real number s. We have sn – s = |Sn – Snp + Snk s| < |Sn – Sni|+|Snk 8|. If we choose n and ng large enough, we should be able to make each term arbitrarily small.
Problem 11.2.22. The th Term Test Show that if an converges then lim an = 0. = 0. in=1
Transcribed Image Text:Problem 11.2.22. The th Term Test Show that if an converges then lim an = 0. = 0. in=1
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
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…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS