帐号 自动登录 找回密码 密码 欢迎注册
 搜索

# [转载] a+b

### 马上注册，结交更多好友，享用更多功能，让你轻松玩转社区。

x

 算下前6项 $$1+\sqrt{5},-\frac{1}{\sqrt{5}},\frac{1}{4} \left(5-\sqrt{5}\right),1+\sqrt{5},-\frac{1}{\sqrt{5}},\frac{1}{4} \left(5-\sqrt{5}\right)$$ 后面步骤你应当会了。

楼主| 发表于 2017-12-1 19:23:49 | 显示全部楼层
 谢谢

 (*https://bbs.emath.ac.cn/thread-9736-1-2.html*) Clear["Global`*"];(*Clear all variables*) a=Sqrt[5]+1 list={a} Do[a=FullSimplify[1/(1-a)];list=Append[list,a],{k,59}] aa=Total@list bb=Times@@list cc=FullSimplify[aa+bb] 复制代码 表是 $\left\{\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}},\sqrt{5}+1,-\frac{1}{\sqrt{5}},\frac{1}{1+\frac{1}{\sqrt{5}}}\right\}$ 求和结果是 $16 \sqrt{5}+\frac{20}{1+\frac{1}{\sqrt{5}}}+20$ 求积的结果是 $1$ 两者的和是 $11 \sqrt{5}+46$

 Sqrt[5]+1//NestList[(1-#)^-1&,#,59]&//(Plus@@#)+(Times@@#)&//Simplify复制代码

 您需要登录后才可以回帖 登录 | 欢迎注册 本版积分规则 回帖后跳转到最后一页

GMT+8, 2018-12-11 21:01 , Processed in 0.055508 second(s), 19 queries .