# Irrationality of reciprocal Fibonacci constant

I read that it was proved that reciprocal Fibonacci constant $$\sum_{n} \frac{1}{F_n} = \frac{1}{1} + \frac{1}{1} + \frac{1}{2} + \frac{1}{3} + \frac{1}{5} + \frac{1}{8} + \frac{1}{13} + \frac{1}{21} + \cdots \approx 3.3598856662 \dots .$$ is irrational.

Can anyone show me the proof or is it too difficult for someone who knows basic number theory?

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I can't read french. – user58512 Jan 22 '13 at 19:08

The general idea is to replace such a sum with a a function, say $f(t)$, and to recover the sum as $f(1)$. The majority of the work is to provide the technical machinery to support inequality (4). This inequality gives an explicit bound on how "close" a rational number can come within a point of interest. With good enough bounds, this is used to show that a value is irrational.