a1C0n+a2C1n+a3C3n+...+an+1Cnn =(2^0+1)C(n,0)+(2^1+1)C(n,1)+...+(2^n+1)C(n,n)
=C(n,0)2^0+C(n,1)2^1+C(n,2)2^2+...+C(n,n)2^n
+C(n,0)+C(n,1)+...+C(n,n)
=(1+2)^n+(1+1)^n=3^n+2^n (由二项式定理逆用)
a1C0n+a2C1n+a3C3n+...+an+1Cnn =(2^0+1)C(n,0)+(2^1+1)C(n,1)+...+(2^n+1)C(n,n)
=C(n,0)2^0+C(n,1)2^1+C(n,2)2^2+...+C(n,n)2^n
+C(n,0)+C(n,1)+...+C(n,n)
=(1+2)^n+(1+1)^n=3^n+2^n (由二项式定理逆用)