设数列{an}满足a0=a,a(n+1)=c·an+1-c,c属于N*,其中a,c是实数,且c≠0(1)求数列{an}的通向(2)设a=1/2,c=1/2,bn=n·(1-an),n∈N*,求数列{bn}的前n项和Sn

问题描述:

设数列{an}满足a0=a,a(n+1)=c·an+1-c,c属于N*,其中a,c是实数,且c≠0
(1)求数列{an}的通向
(2)设a=1/2,c=1/2,bn=n·(1-an),n∈N*,求数列{bn}的前n项和Sn

(1)a(n+1)-1=c(an-1)a0-1=a-1则an-1=(a-1)*c^nan=1+(a-1)*c^n(2)a=c=1/2an=1-(1/2)^(n+1)bn=n*(1/2)^(n+1)Sn=1*(1/2)^2+2*(1/2)^3+...+n*(1/2)^(n+1)2Sn=1*(1/2)^1+2*(1/2)^2+...+(n-1)*(1/2)^nSn=2Sn-Sn=1*(1/2)^1+...