巳知数列{an}的前项和满足2Sn=3(an-1),其中n?N*,1求数列{an}成等差数列;2设数列bn=log3an,若cn=anbn,...

题目

巳知数列{an}的前项和满足2Sn=3(an-1),其中n?N*,1求数列{an}成等差数列;2设数列bn=log3an,若cn=anbn,...
巳知数列{an}的前项和满足2Sn=3(an-1),其中n?N*,1求数列{an}成等差数列;2设数列bn=log3an,若cn=anbn,求数列{cn}的前n项和.

答案

由a1=s1,得a1=3
an=sn-s(n-1),得an=3a(n-1)
数列{an}成等比数列,an=3^n
(2)bn=log3an=n
所以,cn=anbn=n*3^n
Sn=1X3+2X3^2+3X3^3+...+n*3^n
3Sn=1X3^2+2X3^3+3X3^4+...+n*3^(n+1)
Sn=3/4(1-3^n)+3^(n+1)*n/2