Question

这道题第二问是多少？

Answer 1

(18)
1.
a(n+1)=5an-2.3^n
a(n+1) -3^(n+1) = 5(an -3^n)
=> { an -3^n } 是等比数列, q=5
2.
an -3^n = 5^(n-1) .( a1 -3^1)
= 5^n
let
S=1.5^1+2.5^2+...+n.5^n (1)
5S= 1.5^2+2.5^3+...+n.5^(n+1) (2)
(2)-(1)
4S= n.5^(n+1)-(5^1+5^2+...+5^n)
= n.5^(n+1)-(5/4)(5^n-1)
S=(1/4)n.5^(n+1)-(5/16)(5^n-1)
//
bn
=n(an-3^n)
=n.5^n
Tn
=b1+b2+...+bn
=S
=(1/4)n.5^(n+1)-(5/16)(5^n-1)
=5/16 +(5/16)(4n-1).5^n