已知数列{an}满足a1=3,anan-1=2an-1-1,(1)求证{1/an-1}是等差数列
来源:学生作业帮助网 编辑:六六作业网 时间:2024/11/16 19:57:06
已知数列{an}满足a1=3,anan-1=2an-1-1,(1)求证{1/an-1}是等差数列已知数列{an}满足a1=3,anan-1=2an-1-1,(1)求证{1/an-1}是等差数列已知数列
已知数列{an}满足a1=3,anan-1=2an-1-1,(1)求证{1/an-1}是等差数列
已知数列{an}满足a1=3,anan-1=2an-1-1,(1)求证{1/an-1}是等差数列
已知数列{an}满足a1=3,anan-1=2an-1-1,(1)求证{1/an-1}是等差数列
(1)由题意知a(n-1)≠0,∴an=2-1/a(n-1)=2a(n-1)-1/a(n-1) ∴ a(n-1)-1=a(n-1)-1/a(n-1)
∴1/a(n-1)=a(n-1)/a(n-1)-1=a(n-1)-1+1/a(n-1)-1=1+1/a(n-1)-1 ∴1/an-1_1/a(n-1)-1=1
又 1/a1-1=1/2
∵1为常数 ∴1/an-1是以1/2为首项,1位公差的等差数列
(2)(这里就不全部打出来了,毕竟比较麻烦)先根据一算出an=2n+1/2n-1,an再带进去得到bn=1/(2n+1)(2n-1),再代入Sn用裂项相消法,即bn=1/2(1/2n-1_1/2n+1),算出Sn=n/2n+1
已知数列{an}满足a1=1,anan+1=2^n,则a9+a10
数列An满足 根号下AnAn+1 +AnAn+2=4根号下AnAn+1 +An+1An+1 +数列An满足根号下AnAn+1 +AnAn+2=4根号下AnAn+1 +An+1An+1 +3根号下AnAn+1 且A1=1 A2=8 求An通项公式
已知数列满足a1=1,√an-1 - √an = √anan-1 ,求an=
已知数列an满足a1=1/2,anan+1=2an-an+1,求ann+1是下角标
已知数列满足a1=1,根号an-1-根号an=根号anan-1,求an
已知数列{an}满足a1=3,anan-1=2an-1-1,(1)求证{1/an-1}是等差数列
已知数列{an}满足a1=3,anan-1=2an-1-1,(1)求证{1/an-1}是等差数列
数列An满足 根号下AnAn+1 +AnAn+2=4根号下AnAn+1 +An+1An+1 +3根号下AnAn+1 且A1=1,A2=8求An
已知数列{an}满足a1=2且anan+1-2an=0球a2,a3,a4的值
已知数列an 满足a1=1 anan+1=2的n 次方 求a9a10 a9+ a10 已知数列an 满足a1=1 anan+1=2的n 次方 求a9a10 a9+ a10
已知数列an满足a1=1/2,anan-1=an-1-an,求数列an的通项公式
已知数列{an}满足a1=5,anan+1=2的n次方,则a7/a3=
已知数列(An)中,A1=1/3,AnAn-1=An-1-An(n>=2),数列Bn满足Bn=1/An,求数列Bn的通项公式需要详细的步骤
数列{An}满足A1=1/3,且An+1+An^3=3An(1+AnAn+1),求数列{An}的通项公式?)
已知各项均为正数的数列{an},满足a1=3,且(2an+1-an)/(2an-an+1)=anan+1,求an的通项公式
已知数列{an}满足a1=2,且anan+1+an+1-2an=9(n∈N+).(1)求a2、a3、
已知数列{an}满足a1=1,an+1=2an+1(n∈N*). 若函数bn=anan+1,求数列已知数列{an}满足a1=1,an+1=2an+1(n∈N*).若函数bn=anan+1,求数列bn前n项和sn
数列an满足a1=2 ,a2=1,且( an-1 -an )/anan-1 =(an -an+1 )/anan+1 (n大于等于2),求a100 =