Question

已知数列{an}满足a1+2a2+2^2a3+…+2^n-1an=n^2(n∈N*)

Answer 1

1

2^(n-1)an=n^2-(n-1)^2=2n-1

an=(2n-1)/2^(n-1)

2

an=(2n-1)/2^(n-1) 2an=(2n-1)/2^(n-2)

an-1=(2n-3)/2^(n-2) 2an-1=(2n-3)/2^(n-3)

..

a2=3/2 2a2=3

a1=1 2a1=2

..

[2Sn-2a1] - [Sn-(2n-1)/2^(n-1)] =2+1+..+1/2^(n-3)

Sn=