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S=1\cdot 2 2\cdot 3\cdot r 3\cdot 4\cdot r^2 \cdots  n(n 1)r^{n-1}
1-\frac{1}{2} \frac{1}{3}-\cdots \frac{(-1)^{n 1}}{n} \cdots=\log2
a_1=1\ ,\ \ a_n=a_{n-1} n!\cdot n\ \ \ (n\ge2)
f(x)=ax b \ \ \ (a,b \in \mathbf{R})
\frac{dy}{dx} P(x)y=Q(x)