Question

已知数列{an}的通项公式为an=2^(n-1)+1,则a1×Cn0+a2×Cn1……+a(n+1)×Cnn=?

Answer 1

a1×Cn0+a2×Cn1……+a(n+1)×Cnn

=(2^0+1)*C(n,0)+(2^1+1)C(n,1)+(2^2+1)C(n,2)+.+(2^n +1)*C(n,n)

=[2^0*C(n,0)+2^1*C(n,1)+2^2*C(n,2)+.+2^n *C(n,n)]+[C(n,0)+C(n,1)+C(n,2)+.+C(n,n)]

=(1+2)^n+2^n

=3^n+2^n