已知数列{an}满足a1=1,a(n+1)=2an+n+1,设bn=an+n+2证明数列{bn}是等比数列,2.设数列{an}的前n项和为Sn,求an和Sn

Question

已知数列{an}满足a1=1,a(n+1)=2an+n+1,设bn=an+n+2
证明数列{bn}是等比数列,2.设数列{an}的前n项和为Sn,求an和Sn

Answer 1

a(n+1)=2an+n+1an=2a(n-1)+na(n+1)-an=2(an-a(n-1))+1a(n+1)-an+1=2(an-a(n-1))+2a(n+1)-an+1=2(an-a(n-1)+1)a(n+1)-an+1/an-a(n-1)+1=2又bn=an+n+2=a(n+1)-an+1bn-1=a(n-1)+n+1=an-a(n-1)+1bn/bn-1=a(n+1)-an+1/an-...