Harmonious terms

Algebra Level 5

Consider a harmonic progression with distinct real terms. Of the infinite number of statements below regarding that progression, what is the maximum possible number of true statements?

1) The 1st1^\text{st} term of this sequence is equal to 1.
2) The 2nd2^\text{nd} term of this sequence is equal to 2.
3) The 3rd3^\text{rd} term of this sequence is equal to 3.
4) The 4th4^\text{th} term of this sequence is equal to 4.
\qquad\qquad \qquad\qquad \vdots


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