作者ByronC (莫忘初衷)
看板teaching
标题Re: [请益] 几个数学题目公式
时间Sat Mar 21 11:29:50 2009
※ 引述《anchia (我渴望飞..)》之铭言：
: 请问这几题 公式要怎麽写
: 0,1,5,14,30.......
: (加下一个数的平方数)
A2 = A1 + 1^2
A3 = A2 + 2^2
A4 = A3 + 3^2
…
An = An-1 + (n-1)^2
上式全部加起来
An = A1 + Σ(n-1,0) k^2 = 0 + (n-1)(n)(2n-1)/6
: 2,5,11,23.........
: (双倍加1)
A2 = A1*2 + 1
A3 = A2*2 + 1 = A1*2^2 + 2 + 1
A4 = A3*2 + 1 = A1*2^3 + 2^2 + 2 + 1
A5 = A4*2 + 1 = A1*2^4 + 2^3 + 2^2 + 2 + 1
…
An = A1*2^(n-1) + 2^(n-2) + 2^(n-3) + … +1
An = 2*2^(n-1) + 2^(n-2) + 2^(n-3) + … +1
= 2^(n-1) + 2^(n-1) + 2^(n-2) + 2^(n-3) + … +1
= 2^(n-1) + (2^n - 1)/(2-1) = 2^n + 2^(n-1) - 1
: 2,6,12,20,30......
: (连续一对相乘)
A1 = 1*2
A2 = 2*3
…
An = n(n+1)
: 1,1,2,3,5,8,13....
: (费布纳西数列)
寻找系数r,k满足(An - kAn-1) = r (An-1 - kAn-2)意同An = An-1 + An-2
取自网路资料
http://teach.ymhs.tyc.edu.tw/t1086/study/teach/Fibonacci-1.doc
: 谢谢
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※ 编辑: ByronC 来自: 218.170.13.124 (03/21 11:44)