(1)该数列通项an=1+2+3+.+n=1/2*n^2-1/2*n
令bn=1/2*n^2,cn=1/2*n,则an=bn+cn
数列{bn}的前n项和sn'=1/2*(1^2+2^2+3^2+.+n^2)=1/12*n*(n+1)*(2n+1)
数列{cn}的前n项和sn"=1/2*(1+2+3+.+n)=1/4*n*(n+1)
sn=sn'+sn"=1/6*n*(n+1)*(n+2)
(2)xs=x+3x^2+5x^3+.+(2n-1)x^n
s-xs=1+2x+2x^2+2x^3+.+2x^(n-1)-(2n-1)x^n=1-(2n-1)x^n+2*x[1-x^(n-1)]/1-x
s=[1-(2n-1)x^n]/(1-x)+2(x-x^n)/(1-x)^2