李煌——哥德爾定理
1 2 = ( 1 − ( 1 2 ) 1 n ) ∑ k = 1 n ( ( 1 2 ) 1 n ) n − k {\displaystyle {\frac {1}{2}}={\bigg (}1-({\frac {1}{2}})^{\frac {1}{n}}{\bigg )}\sum _{k=1}^{n}{\bigg (}({\frac {1}{2}})^{\frac {1}{n}}{\bigg )}^{n-k}} , n ≥ 1 , n ∈ o d d {\displaystyle n\geq 1,n\in odd}
顯然其特例就當n=1時是我們熟悉的 1 2 = 1 − 1 2 = 1 2 {\displaystyle {\frac {1}{2}}=1-{\frac {1}{2}}={\frac {1}{2}}}
當n=3時是 1 2 = ( 1 − ( 1 2 ) 1 3 ) ( ( 1 2 ) 2 3 + ( 1 2 ) 1 3 + 1 ) {\displaystyle {\frac {1}{2}}={\bigg (}1-({\frac {1}{2}})^{\frac {1}{3}}{\bigg )}{\bigg (}({\frac {1}{2}})^{\frac {2}{3}}+({\frac {1}{2}})^{\frac {1}{3}}+1{\bigg )}}
<<School:李煌數學研究院
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