Let {xn} be a sequence of real numbers. Let yn be the average of the first n-terms: x1+ x2 + Yn + xn Prove that if {xn} converges to xo, then {Yn} also converges to x. (Hint: using the definition of convergence, choose a large threshold N after which |xn – x| is as small as we want, then choose n large enough such that the |x; – x|/n is very small for 1 < i< N.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
Let {xn} be a sequence of real numbers. Let yn be the average of the first
n-terms:
Xi + x2 + .
+ Xn
Yn =
Prove that if {xn} converges to xo, then {yn} also converges to xo. (Hint: using
the definition of convergence, choose a large threshold N after which |Xn – x∞| is as small as
we want, then choose n large enough such that the |x; – x|/n is very small for 1< i < N.)
Transcribed Image Text:Let {xn} be a sequence of real numbers. Let yn be the average of the first n-terms: Xi + x2 + . + Xn Yn = Prove that if {xn} converges to xo, then {yn} also converges to xo. (Hint: using the definition of convergence, choose a large threshold N after which |Xn – x∞| is as small as we want, then choose n large enough such that the |x; – x|/n is very small for 1< i < N.)
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps with 3 images

Blurred answer
Similar questions
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,