Let us copy ... Fourier

General Mathematics
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Tolaso J Kos
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Let us copy ... Fourier

#1

Post by Tolaso J Kos »

Let \( a_n \) be a strictly increasing sequence of positive integers. Prove that:

$$x_n =\frac{1}{a_1} + \frac{1}{a_1 a_2} +\cdots + \frac{1}{a_1 a_2 a_3 \cdots a_n}$$

converges to an irrational number.
Imagination is much more important than knowledge.
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