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waistyle二星初級會員
2010-11-10 17:12#1
題目
(2+X)^n
x^4 terms+x^5terms=14(x^6 terms)
求n
我列的式:
nC4乘2^n-4+nC5乘2^n-5=14(nC6乘2^n-6)
跟住唔識計
有無人可以話我知我列的式o岩唔o岩
同埋點樣計n
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abcdefg111一星新手會員
2010-11-10 18:25#2
如果答案係8,你條式岩
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abcdefg111一星新手會員
2010-11-10 18:33#3
nC4乘2^n-4+nC5乘2^n-5=14(nC6乘2^n-6)
nC4= n(n-1)(n-2)(n-3)/24 nC5=n(n-1)(n-2)(n-3)(n-4)/120
nC6=n(n-1)(n-2)(n-3)(n-4)(n-5)/720
let n(n-1)(n-2)(n-3)=a (方便睇)
(a*2^n-4)/24 + (a*(n-4)*2^n-5)/120 = [14a*(n-4)(n-5) *2^n-6]/720
2^n-4 [1/24 + (n-4)/240] = 2^n-6 [ 14(n-4)(n-5)/720] 抽2^n-4 出黎, 約埋個a
720*4[1/24 +(n-4)/240] =14(n-4)(n-5)
120+ 12n-48 =14n^2 -126n +280
n=8 or 1.85714(rej)