@[ComesAndGoes](/user/715071) 忘说了，不能用若必达
by ComesAndGoes @ 2023-03-19 19:00:45
现在还没找到解$\color{white}{\text{伏笔}}$
by ComesAndGoes @ 2023-03-19 19:10:31
@[ComesAndGoes](/user/715071)
$$
\begin{array}{l}
\lim\limits_{x\to0}\dfrac{m}{1-(x+1)^m}-\dfrac{n}{1-(x+1)^n}\\
=\lim\limits_{x\to0}\dfrac{m}{-mx-\frac{m(m-1)}{2}x^2+o(x^2)}-\dfrac{n}{-nx-\frac{n(n-1)}{2}x^2+o(x^2)}\\
=\lim\limits_{x\to0}\dfrac{1}{-x-\frac{m-1}{2}x^2+o(x^2)}-\dfrac{1}{-x-\frac{n-1}{2}x^2+o(x^2)}\\
=\lim\limits_{x\to0}\dfrac{\frac{m-n}{2}x^2+o(x^2)}{x^2+o(x^2)}\\
=\dfrac{m-n}{2}
\end{array}
$$
by MatrixGroup @ 2023-03-19 19:19:25
@[Breakingtdasc](/user/483824) orz本帖结
by ComesAndGoes @ 2023-03-19 19:19:53