This is dislocation subtraction. If a series is similar to a "mixture" of arithmetic progression and geometric progression, this method can be used.

Pack up, that's it.

-Bn=Bn-2Bn= 1+2+2^2+.....+2^(n- 1)-nX2^n

Then the previous items (except the last item) are geometric series with 1 as the first item and 2 as the common ratio, and the formula can be applied.

So1+2+2+...+2 (n-1) = (2n-1)/(2-1) = (2n-1).

So-bn = 1+2+2+...+2(n- 1)-nx2n =(2n- 1)-nx2n。

So bn = nx2n-(2n-1) = nx2n-2n+1.