Limits #4

Calculus Level 3

if $f(x) = \frac{1}{3}(f(x + 1) + \frac{5}{f(x + 2)})$ and $$f(x) > 0$$ for all real values of x then $lim_{x \to \infty} f(x) = \sqrt\frac{a}{b}$

then a + b =

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