If the coefficient of $x^4$ in the expansion of $\frac{x}{(x-1)^2(x-2)}$ is $\frac{m}{n}$ and $|m|,|n|$ are coprimes, then $\sqrt{|m+n|}=$

If $(-c, c)$ is the set of all values of $x$ for which the expansion of $(7-5 x)^{\frac{-2}{3}}$ is valid, then $5 c+7=$

If $n$ is a positive integer and $f(n)$ is the coefficient of $x^n$ in the expansion of $(1+x)(1-x)^n$, then $f(2023)=$

If $y=\frac{3}{4}+\frac{3 \cdot 5}{4 \cdot 8}+\frac{3 \cdot 5 \cdot 7}{4 \cdot 8 \cdot 12}+\ldots$ to $\infty$, then