设数列{an}满足a1+3a2+3^2a3+```````+3^(n-1)an=n/3(n属于正整数） (1)求数列{an}的通项公式

显示全部楼层 · 2012-4-3 22:57:38

a1+3a2+3^2a3+```````+3^(n-1)an=n/3a1+3a2+3^2a3+```````+3^(n-2)a(n-1)=(n-1)/3两式相减得3^(n-1)an=n/3-(n-1)/33^(n-1)an=n/3-n/3+1/33^(n-1)an=1/33^nan=1an=1/3^nbn=nan=n/3^nsn=1/3^1+2/3^2+3/3^3+.........+n/3^nsn/3=1/3^2+2/3^3+3/3^4+.........+(n-1)/3^n+n/3^(n+1)sn-sn/3=1/3^1+1/3^2+1/3^3+.........+1/3^n-n/3^(n+1)2sn/3=1/3*[1-(...

千问 · 2012-4-3 22:57:38

1an= --------
3^n
n(n+1)sn= ----------------
3(3^n-1)...