設數(shù)列an的首項A1=A,A1不等于1/4,且An+1=(1/2)*An,n為偶數(shù) An+1=An+1/4,n為奇數(shù),記Bn=A2n-1 -1/4,n=1,2,3,4……
設數(shù)列an的首項A1=A,A1不等于1/4,且An+1=(1/2)*An,n為偶數(shù) An+1=An+1/4,n為奇數(shù),記Bn=A2n-1 -1/4,n=1,2,3,4……
(1)求A2,A3
(2)判斷數(shù)列Bn是否為等比數(shù)列,證明你的結(jié)論.
數(shù)學人氣:806 ℃時間:2019-11-06 14:55:38
優(yōu)質(zhì)解答
=5/3a-2/3an 兩邊同乘3
==> 3a=5a-2an 把3個a移到左邊
==> 3a-3a=2a-2an 合并
==> 3(a-a)=2(a-an)
==》 2/3=(a-a)/(a-an)
==> {a-an}是公比為2/3的等比數(shù)列
bn=a-an b=a-a……
a1=2 a2=5/3 ==> b1= a2-a1=5/3-2=-(1/3 )
==> {bn}是首項為-(1/3) 公比為2/3的等比數(shù)列
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