Question

求A(n)=n×2^(n+1)数列的前n项和T(n)

Answer 1

T(n)=1*2^2+2*2^3+……+n×2^(n+1)

2T(n)=1*2^3+2*2^4+……+n×2^(n+2)

两式相减

-T(n)=2^2+2^3+……+2^(n+1)-n*2^(n+2)

=2^(n+2)-4-n*2^(n+2)

T(n)=(n-1)*2^(n+2)+4