作业帮求数列{2n·3的n次方}的前n项和
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求数列{2n·3的n次方}的前n项和
求数列{2n·3的n次方}的前n项和
求数列{2n·3的n次方}的前n项和
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+3^2+...+3^n)
=n.3^(n+1) -(3/2)(3^n-1)
= 3/2 + (3n- 3/2).3^n
an = 2n.3^n
Sn = a1+a2+...+an
=2S
= 3/2 + (3n- 3/2).3^n