Consider the recursively defined sequence (Hn)n>1 where 1. H₁ = 1 2. Hn+1 = Hn+n1 for n ≥ 1 > Compare the quantities H₂n+1 and H2n + 1/2 for n ≥ 0 by creating a table with small values of n. Prove your relation by induction.

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
100%
Consider the recursively defined sequence \((H_n)_{n \geq 1}\) where:

1. \(H_1 = 1\)

2. \(H_{n+1} = H_n + \frac{1}{n+1}\) for \(n \geq 1\)

Compare the quantities \(H_{2n+1}\) and \(H_{2n} + 1/2\) for \(n \geq 0\) by creating a table with small values of \(n\). Prove your relation by induction.
Transcribed Image Text:Consider the recursively defined sequence \((H_n)_{n \geq 1}\) where: 1. \(H_1 = 1\) 2. \(H_{n+1} = H_n + \frac{1}{n+1}\) for \(n \geq 1\) Compare the quantities \(H_{2n+1}\) and \(H_{2n} + 1/2\) for \(n \geq 0\) by creating a table with small values of \(n\). Prove your relation by induction.
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

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,