MathDB

Let

<h_n>

n\in\mathbb N

a harmonic sequence of positive real numbers (that means that every

h_n

is the harmonic mean of its two neighbours h_{n\minus{}1} and h_{n\plus{}1} : h_n\equal{}\frac{2h_{n\minus{}1}h_{n\plus{}1}}{h_{n\minus{}1}\plus{}h_{n\plus{}1}}) Show that: if the sequence includes a member

h_j

, which is the square of a rational number, it includes infinitely many members

h_k

, which are squares of rational numbers.

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Problems(1)