Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
54. If sz is the k th partial sum of the harmonic series, prove that In (k + 1) < S <1+ln k. Hint: 1 1 <-s- if 0

54. If sz is the k th partial sum of the harmonic series, prove that In (k + 1) < S <1+ln k. Hint: 1 1 <-s- if 0

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter9: Sequences, Probability And Counting Theory
Section: Chapter Questions
Problem 13PT: Use the formula for the sum of the first n terms of a geometric series to find k=170.2(5)k1 .
See similar textbooks
icon
Related questions
Question
Problem: 54. If s is thek th partial sum of the harmonic series, prove that In (k + 1) < Sk <1+ In k. Hint: 1 1 1 s- if 0 < m <x <m+ 1. Integrate each member of the т+1 m inequality from m to m + 1;let m take on successively the values 1, 2, ..... n-1, and add the results.
Transcribed Image Text:Problem: 54. If s is thek th partial sum of the harmonic series, prove that In (k + 1) < Sk <1+ In k. Hint: 1 1 1 s- if 0 < m <x <m+ 1. Integrate each member of the т+1 m inequality from m to m + 1;let m take on successively the values 1, 2, ..... n-1, and add the results.
Expert Solution
steps

Step by step

Solved in 3 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer