an=(2n+1)3^(n+2),求Sn
展开全部
let
S=1.3^1+2.3^2+...+n.3^n (1)
3S= 1.3^2+2.3^3+...+n.3^(n+1) (2)
(2)-(1)
2S=n.3^(n+1) -(3^1+3^2+....+3^n)
=n.3^(n+1) -(3/2)(3^n -1)
S= (3/2)n.3^n-(3/4)(3^n -1)
an
=(2n+1)3^(n+2)
=18(n.3^n)+ 9(3^n)
Sn
=a1+a2+...+an
=18S +9[(3/2)(3^n -1)]
=18[(3/2)n.3^n-(3/4)(3^n -1)] + (27/2)(3^n -1)
=27n.3^n -(27/2)(3^n -1) +(27/2)(3^n -1)
=27n.3^n
S=1.3^1+2.3^2+...+n.3^n (1)
3S= 1.3^2+2.3^3+...+n.3^(n+1) (2)
(2)-(1)
2S=n.3^(n+1) -(3^1+3^2+....+3^n)
=n.3^(n+1) -(3/2)(3^n -1)
S= (3/2)n.3^n-(3/4)(3^n -1)
an
=(2n+1)3^(n+2)
=18(n.3^n)+ 9(3^n)
Sn
=a1+a2+...+an
=18S +9[(3/2)(3^n -1)]
=18[(3/2)n.3^n-(3/4)(3^n -1)] + (27/2)(3^n -1)
=27n.3^n -(27/2)(3^n -1) +(27/2)(3^n -1)
=27n.3^n
推荐律师服务:
若未解决您的问题,请您详细描述您的问题,通过百度律临进行免费专业咨询