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Proof: (related to "Upper Bound of Harmonic Series Times Möbius Function")

1 The existence of such an upper bound means that the above series either converges or oscillates in the real interval $[-1,1].$ Which of these two cases is true, can be proven but requires more sophisticated methods we will introduce in analytic number theory. Anticipating the right answer, the series converges and its limit is $0.$

q.e.d

| | | | created: 2019-04-06 22:06:10 | modified: 2019-04-06 22:22:37 | by: bookofproofs | references: [701], [1272]

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Bibliography (further reading)

[1272] Landau, Edmund: “Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie”, S. Hirzel, Leipzig, 1927

[701] Scheid Harald: “Zahlentheorie”, Spektrum Akademischer Verlag, 2003, 3. Auflage