求数列1/5,2/5^2.3/5^3,1/5^4,2/5^5,3/5^6...的前3n项和

本题采用分类求和.a1+a2+a3+a4+a5+a6+……+a(3n-2)+a(3n-1)+a3n=[a1+a4+……+a(3n-2)]+[a2+a5+……+a(3n-1)]+(a3+a6+……+a3n)=[1/5+1/5^4+……+1/5^(3n-2)]+[1/5²+1/5^5+……+1/5^(3n-1)]+[1/5³+1/5^6+…...