Question

这一题怎么写的？具体一些

Answer 1

(1)
a1=1
a(n+1)= 2Sn
Sn =(1/2)a(n+1)
for n≥2
an = Sn -S(n-1)
=(1/2)a(n+1) -(1/2)an
a(n+1) = 3an
an=3^(n-1) .a1
=3^(n-1)
(2)
let
S=1.3^0+2.3^1+....+n.3^(n-1) (1)
3S= 1.3^1+2.3^2+....+n.3^n (2)
(2)-(1)
2S = n.3^n -[ 3^0 +3^1+....+3^(n-1) ]
= n.3^n - (1/2)( 3^n -1)
S =(1/2)n.3^n - (1/4)( 3^n -1)
cn=n.an
Tn
=c1+c2+...+cn
=S
=(1/2)n.3^n - (1/4)( 3^n -1)
=1/4 + [ (1/2)n - 1/4] .3^n