设1×1/3+3×1/9+5×1/27+...+(2n-1)×（1／3＾n)=Sn
3Sn=1+3×1/3+5×1/9+7×1/27+...+(2n-1)×(1/3^n-1)
3Sn-Sn=1+2×1/3+2×1/9+2×1/27+...+2×1/(3^n-1)-(2n-1)×1/3^n
=1-(2n-1)×1/3^n+1-1/(3^n-1)=2Sn
所以Sn除个2就出来了~