Question

数列｛an}中a1=1/3,前n项和Sn满足Sn+1-Sn=(1/3)^n+1(n∈正整数）

Answer 1

S(n+1)-Sn=(1/3)^(n+1)

a(n+1) = (1/3)^(n+1)

an = (1/3)^n

Sn = a1+a2+...+an

= (1/2)[ 1- (1/3)^n ]

S1,t（S1+S2),3(S2+S3）成等差数列

=>

S1+3(S2+S3) = 2t(S1+S2)

(1/3)+ 3(4/9+14/27) = 2t( 1/3 + 4/9)

29/9 = 14t/9

t= 29/14