an=an-a(n-1)+a(n-1)-a(n-2)+a(n-2)-a(n-3)+……a2-a1+a1
=2n-1+2(n-1)-1+……+2*2-1+1
=2(2+3+……+n)-(n-1)+1=n^2
故bn=(-1)^n*n^2
前n项和Sn=b1+b2+……+bn
n为偶数时
Sn=(b1+b2)+(b3+b4)+……+(b(n-1)+bn)
=3+7+11+……+2n-1
=2(n+1)*n/4=n(n+1)/2
n为奇数时
Sn=S(n-1)+n^2=n(n-1)/2-n^2=-n(n+1)/2