Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
Lemma 14.11 Let Sn = integer n. n k=1 = 1+ 1 1 n · + -, where n € N. Then S2 ≥1+ for every positive 2 n

Lemma 14.11 Let Sn = integer n. n k=1 = 1+ 1 1 n · + -, where n € N. Then S2 ≥1+ for every positive 2 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

Please explain the highlighted part of the following proof step by step, It really goes to fast for me on how they suddenly substitute and change variables, please if able really show what is done with each step in detail

 

Lemma 14.11 Let Sn = integer n. Proof n k=1 = 1+ 1 1 n +-, where ne N. Then S2 ≥1+ for every positive 2 n We proceed by induction. For n = 1, $₂¹ = 1 + and so the result holds for n = 1. 1 2 k , where ke N. We show that S₂k+1 ≥ 1+ Assume that s₂k ≥ 1+ that 2 $2k+1 = 1+ 1 2 = $₂k + ≥ S₂k + = S₂k + + 1 2k + 1 1 2k+1 2k 2k+1 1 2k+1 1 2k +2 1 2k+1 + + + S2k + k 1 ≥1+=+ =1+ 2 2 + 1 + 2 k + 1 2 + 1 2k+1 1 ok+1 By the Principle of Mathematical Induction, S2″ ≥1+ integer n. n IN k+1 2 Now observe for every positive
Transcribed Image Text:Lemma 14.11 Let Sn = integer n. Proof n k=1 = 1+ 1 1 n +-, where ne N. Then S2 ≥1+ for every positive 2 n We proceed by induction. For n = 1, $₂¹ = 1 + and so the result holds for n = 1. 1 2 k , where ke N. We show that S₂k+1 ≥ 1+ Assume that s₂k ≥ 1+ that 2 $2k+1 = 1+ 1 2 = $₂k + ≥ S₂k + = S₂k + + 1 2k + 1 1 2k+1 2k 2k+1 1 2k+1 1 2k +2 1 2k+1 + + + S2k + k 1 ≥1+=+ =1+ 2 2 + 1 + 2 k + 1 2 + 1 2k+1 1 ok+1 By the Principle of Mathematical Induction, S2″ ≥1+ integer n. n IN k+1 2 Now observe for every positive
Expert Solution
steps

Step by step

Solved in 4 steps with 4 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