无穷等比数列{an}的各项和为S,若数列{bn}满足bn=a3n-2+a3n-1+a3n,则数列{bn}的各项和为( ) A.S B.3S C.S2 D.S3
问题描述:
无穷等比数列{an}的各项和为S,若数列{bn}满足bn=a3n-2+a3n-1+a3n,则数列{bn}的各项和为( )
A. S
B. 3S
C. S2
D. S3
答
∵无穷等比数列{an}的各项和为S,∴设等比数列{an}的首项为a1,公比为q,则由定义得S=a11−q.∵数列{bn}满足bn=a3n-2+a3n-1+a3n,∴bn+1bn=a3n+1+a3n+2+a3n+3a3n−2+a3n−1+a3n=q3(a3n−2+a3n−1+a3n)a3n−2+a3n...