Question 2
(SWE 2) Let $f(x)=x^n$ where $n$ is a fixed positive integer and $x=1,2,\ldots$. Is the decimal expansion $a=0.f(1)f(2)f(3)\ldots$ rational for any value of $n$?
The decimal expansion of $a$ is defined as follows: If $f(x)=d_1(x)d_2(x)\ldots d_{r(x)}(x)$ is the decimal expansion of $f(x)$, then $a=0.1d_1(2)d_2(2)\ldots d_{r(2)}(2)d_1(3)\ldots d_{r(3)}(3)d_1(4)\ldots$.
The decimal expansion of $a$ is defined as follows: If $f(x)=d_1(x)d_2(x)\ldots d_{r(x)}(x)$ is the decimal expansion of $f(x)$, then $a=0.1d_1(2)d_2(2)\ldots d_{r(2)}(2)d_1(3)\ldots d_{r(3)}(3)d_1(4)\ldots$.