数列bn的前n项和为Tn,6Tn=(3n+1)bn+2,求bn
问题描述:
数列bn的前n项和为Tn,6Tn=(3n+1)bn+2,求bn
答
当n≥2时,有bn=Tn-T(n-1)所以由6Tn=(3n+1)bn+2得6T(n-1)=(3(n-1)+1)b(n-1)+2上两式相减得6(Tn-T(n-1)=(3n+1)bn-(3n-2)b(n-1)即6bn=(3n+1)bn-(3n-2)b(n-1)即(3n-5)bn=(3n-2)b(n-1)bn/(3n-2)=b(n-1)/(3n-5)bn/(3n-2)=b...