# Fibonacci Decimals

Algebra Level 4

$\displaystyle \frac{1}{10^0} + \frac{1}{10^1} + \frac{2}{10^2} + \frac{3}{10^3} + \frac{5}{10^4} + \frac{8}{10^5} + \frac{13}{10^6} + \cdots$

If the value of the sum above can be expressed as $$\dfrac mn$$ for positive coprime integers $$m$$ and $$n$$, find $$\dfrac{n + 1}{\sqrt{m}}$$.

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