數學(幫幫手)唔識!!點做?

2010-11-03 11:25 pm
given 9C0=1,9C1=9,9C2=36,9C3=84,and 9C4=126,construct the pascal triangle from 9Ci to 11Ci ??

回答 (1)

2010-11-04 12:46 am
✔ 最佳答案
運用兩條恆等式 : nCm = nC(n-m)........(1)nCm + nC(m+1) = (n+1)C(m+1).............(2)運用 (1) , 9C5 = 9C4 = 126 , 9C6 = 9C3 = 84 ......得 9Ci 一行為 : 1 9 36 84 126 126 84 36 9 1 運用 (2) , 10C1 = 9C0 + 9C1 = 1 + 9 = 10 , 10C2 = 9C1 + 9C2 = 9+36 = 45 ,得 10Ci 一行為 : 1 (1+9) (9+36) (36+84) (84+126) (126+126) (126+84) (84+36) (36+9) (9+1) 1==> 1 10 45 120 210 252 210 120 45 10 1 類似地 , 11Ci 一行為 :1 (1+10) (10+45) (45+120) (120+210) (210+252) (252+210) (210+120) (120+45) (45+10) (10+1) 1==> 1 11 55 165 330 462 462 330 165 55 11 1


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