# 2008-2 Strange representation (9/11)

Prove that if x is a real number such that $$0<x\le \frac12$$, then x can be represented as an infinite sum

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

where each $$n_k$$ is an integer such that $$\frac{n_{k+1}}{n_k}\in \{3,4,5,6,8,9\}$$.

x가 $$0<x\le \frac12$$을 만족하는 실수일때, x는 아래와 같은 무한급수로 표현할 수 있음을 보여라.

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

여기서 각 $$n_k$$는 정수이며 $$\frac{n_{k+1}}{n_k}\in \{3,4,5,6,8,9\}$$을 만족한다.

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