粘来的证明

\[\huge{数学智熄操作} \]

$$1.\ 展开\ (a+b)^n。$$

$$解：(\ \ \ \ \ \ \ a\ \ \ \ \ \ \ +\ \ \ \ \ \ \ b\ \ \ \ \ \ \ )\ \ \ \ \ \ \ ^n。$$

$$2.\ 已知\ 0<x<y<1，填入不等号：$$

$$\frac{1}{ln (1-x^2)} \_ \_ \_ \_ \frac{1}{\ln (1-y^2)}$$

$$解：\frac{1}{\ln (1-x^2)}\ \ \ \ \ne\ \ \ \ \frac{1}{\ln (1-y^2)}$$

$$ 3.\ 已知\ x^2-x-1=0，求\ x。$$

$$解：x，求你了。$$

$$4.\ 判断\sum_{n=1}^{\infty}\dfrac{\sin x}{n}\ 的敛散性。$$

$$解：\sum_{n=1}^{\infty}\dfrac{\sin x}{n}$$

$$（分数上下同时消掉\ n）$$

$$=\sum_{n=1}^{\infty}\text{six}$$

$$=\sum_{n=1}^{\infty}6\ \ $$

$$\ \ \ \ \ \ \ \ \ \ \ \ \ =6+6+6+...$$

$$故发散。$$

$$5.\ 已知\frac{1}{0}=\infty，证明\frac{1}{\infty}=0。$$

$$证明：$$

$$（请横过来看）$$

$$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 8\ \ \ \ \ \ \ \ \ \ \ \ 8\ \ \ -8=\ \ \ \ 0\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0$$

$$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ||\ \ \ \rightarrow\ \ ||\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ||\ \ \ \ \ \ \ \rightarrow\ \ \ \ ||\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $$

$$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ -|0\ \ \ \ \ \ -10\ -8=-18\ \ \ \ \ \ \ \ \ \ \ -|8$$

$$6.\ 已知$$

$$\lim_{x\rightarrow8}\dfrac{1}{x-8}=\infty，$$

$$那么$$

居中失败了TwT

\(\lim_\limits{ x\rightarrow5}\dfrac{1}{x-5}=\) （把5横过来）

$$7.\ 求\ 3\times9。$$

$$解:3\times9$$

$$\ \ \ =3\sqrt{81}$$

$$\ \ =3/\overline{81}$$ 这是竖式中的除法

$$=27.\ $$