设:S=Cn^0+3Cn^1+5Cn^2+…+(2n+1)Cn^n S=(2n+1)Cn^n+(2n-1)Cn^(n-1)+…+3Cn^1+Cn^0
=(2n+1)Cn^0+(2n-1)Cn^1+…+3Cn^(n-1)+Cn^n
两式相加,得:
2S=(2n+2)[Cn^0+Cn^1+…+Cn^n]=(2n+2)2^n
则:S=(n+1)2^n
设:S=Cn^0+3Cn^1+5Cn^2+…+(2n+1)Cn^n S=(2n+1)Cn^n+(2n-1)Cn^(n-1)+…+3Cn^1+Cn^0
=(2n+1)Cn^0+(2n-1)Cn^1+…+3Cn^(n-1)+Cn^n
两式相加,得:
2S=(2n+2)[Cn^0+Cn^1+…+Cn^n]=(2n+2)2^n
则:S=(n+1)2^n