MathDB

7. Prove that any real number x satysfying the inequalities

0<x\leq 1

can be represented in the form

x= \sum_{k=1}^{\infty}\frac{1}{n_k}

where

(n_k)_{k=1}^{\infty}

is a sequence of positive integers such that

\frac{n_{k+1}}{n_k}

assumes, for each

k

, one of the three values

2,3

4

. (N. 14)

Problem Statement