Arithmetic - Harmonic progression

General Mathematics
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Tolaso J Kos
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Arithmetic - Harmonic progression

#1

Post by Tolaso J Kos »

Consider the harmonic sequence

$$1, \frac{1}{2}, \frac{1}{3}, \cdots, \frac{1}{n}, \cdots$$

Prove that if we pick dinstinct terms of the above sequence we can construct an arithmetic progression sequence of as large (finite) length as we want.
Imagination is much more important than knowledge.
Demetres
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Re: Arithmetic - Harmonic progression

#2

Post by Demetres »

Just observe that $\displaystyle{\frac{1}{n!}, \frac{2}{n!}, \ldots, \frac{n}{n!}}$ are all distinct terms of the sequence.
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