Question

数列{lg[10^(n-1)/3^(n)]}的前n项和Sn=

Answer 1

a1=-lg3

an=lg[10^(n-1)/3^(n)]=lg[10^(n-1)]-lg{3^(n)}=(n-1)-nlg3

an-1=(n-2)-(n-1)lg3

d=an-an-1=1-lg3=1-lg3

Sn=na1+n(n-1)(1-lg3)/2=n(n-1)(1-lg3)/2-nlg3