数学排列组合：C(m,n+1):C(m,n):C(m-2,n)=4:2:1求m,n值.m右上n右下角

数学排列组合：C(m,n+1):C(m,n):C(m-2,n)=4:2:1求m,n值.m右上n右下角
数学排列组合：C(m,n+1):C(m,n):C(m-2,n)=4:2:1求m,n值.m右上n右下角

数学排列组合：C(m,n+1):C(m,n):C(m-2,n)=4:2:1求m,n值.m右上n右下角
因为C(m,n+1)=C(m,n)+C(m-1,n)
[C(m,n+1)]/C(m,n)=[C(m,n)+C(m-1,n)]/C(m,n)
=1+C(m-1,n)/C(m,n)=4/2=2
所以C(m-1,n)=C(m,n)
所以（m-1）+m=2m-1=n;
所以
[C(m,n)]/[C(m-2,n)]
=[C(m,2m-1)]/C(m-2,2m-1)
=2/1
=2,
C(m,2m-1)=(2m-1)!/{m![(2m-1)-m]!}
=(2m-1)!/[m!(m-1)!]
C(m-2,2m-1)
=(2m-1)!/{(m-2)![(2m-1)-(m-2)]!}
=(2m-1)!/[(m-2)!(m+1)!]
所以
[C(m,n)]/[C(m-2,n)]
={(2m-1)!/[m!(m-1)!]}/{(2m-1)!/[(m-2)!(m+1)!]}
=[(m-2)!(m+1)!]/[m!(m-1)!]
=(m+1)/(m-1)
=2
所以
(m+1)/(m-1) =2
m=3
n=2m-1=5