係数が何の値か気付けるかな

\begin{align*} \frac{1}{x^{5}}+\frac{5}{x^{4}}+\frac{10}{x^{3}}+\frac{10}{x^{2}}+\frac{5}{x}+1 & =C\left(5,5\right)\left(\frac{1}{x}\right)^{5}+C\left(5,4\right)\left(\frac{1}{x}\right)^{4}+C\left(5,3\right)\left(\frac{1}{x}\right)^{3}+C\left(5,2\right)\left(\frac{1}{x}\right)^{2}+C\left(5,1\right)\left(\frac{1}{x}\right)^{1}+C\left(5,0\right)\left(\frac{1}{x}\right)^{0}\\ & =\left(1+\frac{1}{x}\right)^{5}\\ & =\left(1+\frac{1}{1+\sqrt[5]{2}+\sqrt[5]{4}+\sqrt[5]{8}+\sqrt[5]{16}}\right)^{5}\\ & =\left(1+\frac{1}{1+2^{\frac{1}{5}}+2^{\frac{2}{5}}+2^{\frac{3}{5}}+2^{\frac{4}{5}}}\right)^{5}\\ & =\left(1+\frac{1-2^{\frac{1}{5}}}{1-2^{\frac{5}{5}}}\right)^{5}\\ & =\left(1-\left(1-2^{\frac{1}{5}}\right)\right)^{5}\\ & =\left(2^{\frac{1}{5}}\right)^{5}\\ & =2 \end{align*}