Find the fraction where the decimal expansion is infinite? Find the fraction with integers for the numerator and denominator, where the decimal expansion is $0.11235.....$ 
The numerator and denominator must be less than $100$. 
Find the fraction. 
I believe I can use generating functions here to get $1+x+2x^2+3x^3+5x^4+.....$, but I do not know how to apply it. 

These are fractions $f$ with $11235/100000\le f<11236/100000.$ A direct, if slow, method for counting these would be
$$
\sum_{d=1}^{100}\left\lfloor\frac{100000d}{11235}\right\rfloor-\left\lfloor\frac{100000d}{11236}\right\rfloor
$$
or
sum(d=1,100,100000*d\11235-100000*d\11236)

