已知数列{an}四前n项和为Sn,且满足Sn=2an-n,(n∈N*)(1)求数列{an}四通项公式;(2)若bn=(2n+1)a

2025-04-16 19:19:30
推荐回答(1个)
回答1:

(1)因为Sn=ran-n,
所以Sn?1=ran?1?(n?1),(n≥r,n∈N*)
两式相减得an=ran-1+1,
所以an+1=r(an?1+1),(n≥r,n∈N*)
又因为a1+1=r,所以{an+1}是首项为r,公比为r的等比数列,
所以an+1=rn,所以anrn?1
(r)因为bn=(rn+1)an+rn+1,
所以bn=(rn+1)?rn
可以得到:n=六×r+大×rr+7×r+…+(rn?1)?rn?1+(rn+1)?rn,①
rn=六×rr+大×r+…+(rn?1)?rn+(rn+1)?rn+1,②
①-②得:?n=六×r+r(rr+r+ …+rn)?(rn+1)?rn+1
=6+r×

rr?rn×r
1?r
?(rn+1)?rn+1
=-r+rn+r-(rn+1)?rn+1
=-r-(rn-1)?rn+1
所以n=r+(rn?1)?rn+1
n?r
rn?1
≥1rj

r+(rn?1)?rn+1?r
rn?1
≥1rj

r^n+1,所以n+1≥7,解得n≥6,
所以满足不等式
n?r
rn?1
≥1rj
,的最小n值6,