1 1 Let Hn = 1+ 2 1 +... + be the n-th Harmonic number. Prove that H2n <1+n for all nonnegative integers n.

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter3: Groups
Section3.2: Properties Of Group Elements
Problem 30E: 30. Prove statement of Theorem : for all integers .
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prove by induction
1
Let Hn = 1+
2
1
+...+
3
1
be the n-th Harmonic number.
n
Prove that H2n <1+n for all nonnegative integers n.
Transcribed Image Text:1 Let Hn = 1+ 2 1 +...+ 3 1 be the n-th Harmonic number. n Prove that H2n <1+n for all nonnegative integers n.
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