Question

高一数学的数列求通项公式已知数列｛an｝的前n项和为Sn,且㏒（Sn＋1）＝n+1,求通项公式

Answer 1

log(Sn+1) =n+1

Sn +1 = 10^(n+1) (1)

n=1,

a1+1=100

a1=99

S(n-1) +1 = 10^n (2)

(1)-(2)

an = 9.10^n

ie

an =99 ; n=1

=9.10^n ; n=2,3,4,...