Question

数列3*2+6*4+9*8+...+3n*2^n求和

Answer 1

S=3*2+6*4+9*8+...+3n*2^n

2S=3*4+6*8+……+3(n-1)*2^n+3n*2^(n+1)

-S=3*2+3*4+3*8+……+3*2^n-3n*2^(n+1)

S=3n*2^(n+1)-6*[(1-2^(n-1))/(1-2)]

=3n*2^(n+1)-6*2^(n-1)+6