设b>0,数列an满足a1=b,an=nban-1/an-1+n-1(n≥2)求数列an通向公式.
来源:学生作业帮 编辑:灵鹊做题网作业帮 分类:综合作业 时间:2024/04/27 23:04:31
设b>0,数列an满足a1=b,an=nban-1/an-1+n-1(n≥2)求数列an通向公式.
an=nba(n-1)/(a(n-1)+n-1)
an.a(n-1) +(n-1)an = nba(n-1)
1+(n-1)[ 1/a(n-1)] = nb (1/an)
(n-1)( 1/a(n-1) +[1/(1-b)]/(n-1)) = nb( 1/an + [1/(1-b)]/n )
( 1/an + [1/(1-b)]/n ) /( 1/a(n-1) +[1/(1-b)]/(n-1)) = (1/b) (n-1)/n
( 1/an + [1/(1-b)]/n )/(1/a1- 1/(1-b)) = (1/b) 1/n
( 1/an + [1/(1-b)]/n ) = (1-2b)/[b^2(1-b)] (1/n)
1/an = (1/n) [1/(1-b)] [ (1-2b)/b^2 - 1]
an = n(1-b)/ [ (1-2b)/b^2 - 1]
= n(1-b) b^2/ (1-2b-b^2)
an.a(n-1) +(n-1)an = nba(n-1)
1+(n-1)[ 1/a(n-1)] = nb (1/an)
(n-1)( 1/a(n-1) +[1/(1-b)]/(n-1)) = nb( 1/an + [1/(1-b)]/n )
( 1/an + [1/(1-b)]/n ) /( 1/a(n-1) +[1/(1-b)]/(n-1)) = (1/b) (n-1)/n
( 1/an + [1/(1-b)]/n )/(1/a1- 1/(1-b)) = (1/b) 1/n
( 1/an + [1/(1-b)]/n ) = (1-2b)/[b^2(1-b)] (1/n)
1/an = (1/n) [1/(1-b)] [ (1-2b)/b^2 - 1]
an = n(1-b)/ [ (1-2b)/b^2 - 1]
= n(1-b) b^2/ (1-2b-b^2)
设b>0,数列an满足a1=b,an=nban-1/an-1+n-1(n≥2)求数列an通向公式.
设b>0,数列an满足a1=b,an=nban-1/an-1+n-1(n≥2)求数列an通向公式
b>0,数列{an}满足:a1=b,an=nban-1/(an-1+n-1)(n≥2).⑴求数列{an}的通项公式
设b>0,数列an满足a1=b,an=(nban-1)/(an-1 +2n -2)(n≥2).⑴求数列{an}的通项公式
设b>0,数列{an}满足:a1=b,an=nban-1/(an-1+n-1)(n≥2).⑴求数列{an}的通项公式 ⑵
已知数列{an}满足a1=b,an=nban-1/an-1+n-1(n大于等于2),求数列an的通项公式
数列an满足a1=1/2 a(n+1)=1/2-an (1)求数列an的通向公式 (2)设数列an的前n项为Sn 证明S
已知数列{An},An+1=2(n+1)+An,求数列An通向
已知数列{an},an不等于0,a1=3,(1/an+1)=2+(1/an),n为自然数,求an通向公式
设数列{an}满足a1=2,an+1-an=3*2^2n-1 (1)求数列{an}的通项公式 (2)b=nan,求数列{
数列an满足a1=2an+1=2n+1an/【(n+1/2)an+1+2n】(1)bn=2n/an求bn通向(2)设cn
数列an,a1=1,a(n+1)=an/(2an+1),求通向an