Easy to understand, I have a poor foundation, too abstruse to understand ~

Easy to understand, I have a poor foundation, too abstruse to understand ~

Let me give you an example
For example, an = n, BN = 2 ^ n
Finding the sum of the first n terms of an * BN
A1*B1+...+An*Bn
=1*2^1+2*2^2+3*2^3.+(n-1)*2^(n-1)+n*2^n
2(A1*B1+...+An*Bn)
= 1*2^2+2*2^3.+(n-2)*2^(n-1)+(n-1)*2^n+n*2^(n+1)
Below minus above
A1*B1+...+An*Bn
=1*2^1+n*2^(n+1)-(2^2+2^3+...+2^n)
Then apply the summation formula of equal ratio sequence to get the answer
What's the matter? Do you understand