2^n-1
證明對於所有自然數n: (n+1) (n+2) (n+3) ...(2n) = 2^n (1)(3)(5)...(2n-1) 方法一： @ @ wang620628. ,If 2k + 1 is prime and k > 0, then k must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. · Euler proved that every factor of Fn ... ,Here we prove that if 2^n-1 is prime, then so is n. This is a key proof in understanding the Mersenne numbers. ,So (*) works for n = 1. Assume, for n = k, that (*) holds; that is, that. 2 + 22 + 23 ... ,In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer ... ,关于1^2+2^2+3^2+…+n^2的多种推导证明方法- 关于前n 个自然数的平方和公式的证明方法湘西州花垣县边城高级中学-张秀洲在《数列》教学过程中，大家都能 ... ,圖解連續正整數平方和公式. 附圖，由5個正方形與5個小長方形組合成大長方形，5個正方形的邊長分別是1、2、3、4、5，5個小長方形的邊長規格分別 ... ,在數學中，正整数的階乘（英語：factorial）是所有小於及等於該數的正整數的積，計為n!，例如5的階乘計為 5!，其值為120：. 5 ! = 5 × 4 × 3 × 2 × 1 = 120 .
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 2^n-1 相關參考資料
(3)(5)...(2n-1) @ 信欣茗數學園地 - 隨意窩
證明對於所有自然數n: (n+1) (n+2) (n+3) ...(2n) = 2^n (1)(3)(5)...(2n-1) 方法一： @ @ wang620628. https://blog.xuite.net Fermat number - Wikipedia
If 2k + 1 is prime and k > 0, then k must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. · Euler proved that every factor of Fn ... https://en.wikipedia.org If 2^n-1 is prime, then so is n - The Prime Pages
Here we prove that if 2^n-1 is prime, then so is n. This is a key proof in understanding the Mersenne numbers. https://primes.utm.edu Induction Proofs: Worked examples - Purplemath
So (*) works for n = 1. Assume, for n = k, that (*) holds; that is, that. 2 + 22 + 23 ... https://www.purplemath.com Mersenne prime - Wikipedia
In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form Mn = 2n − 1 for some integer ... https://en.wikipedia.org 关于1^2+2^2+3^2+…+n^2的多种推导证明方法 - 百度文库
关于1^2+2^2+3^2+…+n^2的多种推导证明方法- 关于前n 个自然数的平方和公式的证明方法湘西州花垣县边城高级中学-张秀洲在《数列》教学过程中，大家都能 ... https://wenku.baidu.com 圖解連續正整數平方和公式- n - 昌爸工作坊
圖解連續正整數平方和公式. 附圖，由5個正方形與5個小長方形組合成大長方形，5個正方形的邊長分別是1、2、3、4、5，5個小長方形的邊長規格分別 ... http://www.mathland.idv.tw 階乘- 维基百科，自由的百科全书
在數學中，正整数的階乘（英語：factorial）是所有小於及等於該數的正整數的積，計為n!，例如5的階乘計為 5!，其值為120：. 5 ! = 5 × 4 × 3 × 2 × 1 = 120 . https://zh.wikipedia.org |