For example, an = n bn = 2 n

Find the sum of the first n terms of a *Bn

A 1*B 1+...+An*Bn

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

2(A 1*B 1+...+An*Bn)

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

Subtract from the bottom and get from the top.

A 1*B 1+...+An*Bn

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

Then the answer is obtained by applying the summation formula of equal proportion series.

What's the point? You got it?