Question

数列{an},a1+a2+...+an=3n^2,求an

Answer 1

1.Sn=3n^2 Sn-1=3n^2-6n+3

Sn-Sn+1=an=6n-3

2.Sn=3/2+4/2^2+5/2^3+...+[n+2]/2^n

2Sn=3/2^2+4/2^3...+(n+1)/2^n+(n+2)/2^(n+1)

Sn-2Sn=-Sn={4-1/2^(n-1)}/2-(n+2)/2^(n+1)

Sn=(n+2)/2^(n+1)+1/2^n-2