有冇人可以俾呢個 Sequence 條 equation 我
0 1 4 10 20 35 56 84
n1 n2 n3 n4 n5 n6 n7 n8
0 1 4 10 20 35 56 84
1 3 6 10 15 21 28 First difference (triangle number)
2 3 4 5 6 7 Second difference
1 1 1 1 1 Third difference
Maths 求救 : Sequence [4個 differnence]
2008-02-08 11:22 am
回答 (1)
2008-02-08 5:51 pm
✔ 最佳答案
The general formula for the nth term is:T(n)=T(1) + D1(1)*(n-1)/1! + D2(1)*(n-1)(n-2)/2! + D3(1)*(n-1)(n-2)(n-3)/3! + ...
where
T(1)=first term,
D1(1)=first term of the 1st difference
D2(1)=first term of the 2nd difference, etc.
T(1)=0
D1(1)=1
D2(1)=2
D3(1)=1
T(n)=0+1*(n-1)+2*(n-1)(n-2)/2+1*(n-1)(n-2)(n-3)/6
=n(n2-1)/6
T(1)=0;
T(2)=1;
T(3)=4;
T(4)=10; ...
收錄日期: 2021-04-13 15:07:29
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20080208000051KK00356