算术入门

$$\begin{gathered} \textbf{算术入门}\kern{200pt} \text{fixed by SunSkydp} \cr\boxed{\begin{aligned} &\kern{15pt} \begin{aligned} \cr &\text{先假设你有一只兔子。}\cr \cr&\Huge{🐇} \cr &\text{假设现在有人又给了你另一个兔子。}\cr \cr&\Huge{🐇🐇}\cr &\text{现在，数一数你所拥有的兔子数量，你会得到结果是两只。也就是说}\cr &\text{一只兔子加一只兔子等于两只兔子，也就是一加一等于二。}\cr &{\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 1+1=2} \cr &\text{这就是算术的运算方法了。}\cr \cr &\text{那么，现在你已经对算术的基本原理有了一定的了解，就让我们来看}\cr &\text{一看下面这个简单的例子，来把我们刚刚学到的东西运用到实践中吧。}\kern{15pt}\cr &\underline{\kern{310pt}}\cr \end{aligned}\cr &\kern{10pt}\boxed{\stackrel{\normalsize\quad\textbf{试试看!}\quad}{\normalsize\quad\text{例题 1.7}\quad}}\cr &\begin{gathered} \kern{5pt}\log \Pi(N)=\Big(N+\dfrac{1}{2}\Big)\log N -N+A-\int_{N}^{\infty}\dfrac{\overline{B}_1(x){\rm d} x}{x}, A=1+\int_{1}^{\infty}\dfrac{\overline{B}_1(x){\rm d} x}{x} \cr \log \Pi(s)=\Big(s+\dfrac{1}{2}\Big)\log s-s+A-\int_{0}^{\infty}\dfrac{\overline{B}_1(t){\rm d} t}{t+s} \end{gathered}\cr &\kern{5pt}\begin{aligned} \log \Pi(s)=&\lim_{n\to \infty}\Big[s \log(N+1)+\sum_{n=1}^{N}\log n-\sum_{n=1}^{N}\log(s+n)\Big]\cr =&\lim_{n\to \infty}\Big[s \log (N+1)+\int_{1}^{N}\log x {\rm d} x-\dfrac{1}{2}\log N +\int_{1}^{N}\dfrac{\overline{B}_1{\rm d} x}{x}\cr &-\int_{1}^{N}\log(s+x){\rm d} x-\dfrac{1}{2}[\log(s+1)+\log(s+N)]\cr &-\int_{1}^{N}\dfrac{\overline{B}_1(x){\rm d} x}{s+x}\Big]\cr =&\lim_{n\to \infty}\Big[s\log(N+1)+N\log N-N+1+\dfrac{1}{2}\log N+\int_{1}^{N}\dfrac{\overline{B}_1(x){\rm d} x}{x} \cr &-(s+N)\log(s+N)+(s+N)+(s+1)\log(s+1)\cr &-(s+1)-\dfrac{1}{2}\log(s+1)-\dfrac{1}{2}\log(s+N)-\int_{1}^{N}\dfrac{\overline{B}_1(x){\rm d} x}{s+x}\Big]\cr =&\Big(s+\dfrac{1}{2} \Big)\log(s+1)+\int_{1}^{\infty}\dfrac{\overline{B}_1(x){\rm d} x}{x}-\int_{1}^{N}\dfrac{\overline{B}_1(x){\rm d} x}{s+x}\cr &+\lim_{n \to \infty}\Big[s\log(N+1)+\Big(N\dfrac{1}{2}\Big)\log N\cr &-\Big(s+N+\dfrac{1}{2}\Big)\log(s+N)\Big]\cr =&\Big(s+\dfrac{1}{2}\Big)\log(s+1)+(A-1)-\int_{1}^{\infty}\dfrac{\overline{B}_1(x){\rm d} x}{s+x}\cr &+\lim\Big[s\log\dfrac{N+1}{2}-\Big(N+\dfrac{1}{2}\Big)\log\Big(1+\dfrac{s}{2}\Big)\Big] \end{aligned} \end{aligned}}\cr \textbf{假如让写计算机编程书籍的那些人来出教程} \end{gathered}$$

$$\tiny{\color{gray}以上内容非图片，为\color{white}可\color{white}复\color{white}制\color{gray} \LaTeX 公式}$$