Question 3The set of all possible values of $x$ for which the sum of the infinite series $$1+\frac16(x^2-5x)+\frac1{6^2}(x^2-5x)^2+\frac1{6^3}(x^2-5x)^3+\cdots$$ exists can be expressed as $(a,b)\cup(c,d)$, where $a\lt b\lt c\lt d$. Find $d-a$.