54. If s, is the kth partial sum of the harmonic series. prove that In(k + 1) < S < 1 + In k. Hint: 1 1 if 0 < m < x Sm + 1. Integrate - т+1 each member of the inequality from m to m + 1; let m take on successively the values 1, 2, . . . , n - 1, and add the results. m 55. Use the method of Exercise 54 to estimate the sum 100 1 1 50 + ... + 100 m=50 m 51
54. If s, is the kth partial sum of the harmonic series. prove that In(k + 1) < S < 1 + In k. Hint: 1 1 if 0 < m < x Sm + 1. Integrate - т+1 each member of the inequality from m to m + 1; let m take on successively the values 1, 2, . . . , n - 1, and add the results. m 55. Use the method of Exercise 54 to estimate the sum 100 1 1 50 + ... + 100 m=50 m 51
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.5: The Binomial Theorem
Problem 37E
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answer the #55 thank you
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