已知C(4,n).C(5,n)C(6,n)成等差数列,求C(12,n)的值.
问题描述:
已知C(4,n).C(5,n)C(6,n)成等差数列,求C(12,n)的值.
答
C(4,n)+C(6,n) =2C(5,n)n(n-1)(n-2)(n-3)/4! + n(n-1)(n-2)(n-3)(n-4)(n-5)/6! = 2[n(n-1)(n-2)(n-3)(n-4)/5!]1+(n-4)(n-5)/30=2(n-4)/530+(n-4)(n-5)= 12(n-4)n^2-21n+98=0(n-14)(n-7)=0n=14 or 7 (rejected)C(12,n...C(4,n)+C(6,n) =2C(5,n)n(n-1)(n-2)(n-3)/4! + n(n-1)(n-2)(n-3)(n-4)(n-5)/6! = 2[n(n-1)(n-2)(n-3)(n-4)/5!]1+(n-4)(n-5)/30=2(n-4)/530+(n-4)(n-5)= 12(n-4)我对数学不通,看不懂,能。。。