Question

高中数学，怎么这道题我这样做做不出来呢

Answer 1

(I)
a(n+1)= Sn + 3^n
S(n+1)-Sn =Sn + 3^n
S(n+1) -3^(n+1)= 2( Sn - 3^n)
=> {Sn-3^n} 是等比数列， q=2
(II)
Sn-3^n = 2^(n-1) .(S1 -3)
Sn-3^n = 2^(n-1) .(a1 -3)
Sn =3^n + 2^(n-1) .(a1 -3)
for n>=2
an = Sn - S(n-1)
=3^n + 2^(n-1) .(a1 -3) - 3^(n-1) + 2^(n-2) .(a1 -3)
= 2.3^(n-1) + (a1-3).2^(n-2)
n=2
a2 -a1 =6 + (a1-3) -a1 =3 >0
for n>=3
an - a(n-1) >0
2.3^(n-1) + (a1-3).2^(n-2) - 2.3^(n-2) + (a1-3).2^(n-3) >0
4.3^(n-2) +(a1-3).2^(n-3) >0
=> a1< 3