Re: [問題] 指數率的問題
※ 引述《walter0217 (萌香は俺の嫁)》之銘言：
: 我有上啞唬找了指數率的公式，但是也只有基本的
: 因為在Big Book上也有看到類似的題目，滿擔心的...
: 譬如
: 5 6
: 6 5 這種類型的有快速解法嗎?
結論而言，
x > y ; x,y > 3 ; 則 x^y < y^x
証明如下
it suffices to proof that n^(n+1) - (n+1)^n > 0 (use induction on y-x)
and note that the binomial coeffecient C(n,m) =< n^m =< n^n
in particular, C(n,2) + 1 = n*(n-1)/2 + 1 < n^2 for n > 3
hence,
n^(n+1) - (n+1)^n
= n^(n+1) - C(n,0)*n^n - C(n,1)*n^(n-1) - ... - C(n,n-1)*n^1 - 1
= (n^n - C(n,0)*n^n) - (n^n - C(n,1)*n^(n-1)) - (n^n - C(n,2)*n^(n-2) - 1)
(n^n - C(n,3)*n^(n-3)) - ... - (n^n - C(n,n-1)*n^1)
> 0 (since each term is greater than 0)
and the statement follows
: 還有就是log...
: 雖然有公式，可是我對這兩種題型完全沒輒 ┐(─＿─)┌
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 125.225.70.144
→
04/06 22:34, , 1F
04/06 22:34, 1F
推
04/06 23:11, , 2F
04/06 23:11, 2F
推
04/06 23:53, , 3F
04/06 23:53, 3F
推
04/06 23:57, , 4F
04/06 23:57, 4F
推
04/07 00:06, , 5F
04/07 00:06, 5F
→
04/07 00:17, , 6F
04/07 00:17, 6F
→
04/08 20:43, , 7F
04/08 20:43, 7F
討論串 (同標題文章)
GRE 近期熱門文章
PTT職涯區 即時熱門文章
125
248