已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,(1)求a2,a3的值 (2)求证:数列1/an是等差数列,(3)求a100
来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/21 13:32:28
已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,(1)求a2,a3的值 (2)求证:数列1/an是等差数列,(3)求a100
已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,
已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,(1)求a2,a3的值 (2)求证:数列1/an是等差数列,(3)求a100
已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,已知函数f(x)=3x/x+3,设an+1=f(an),且a1=1/2,(1)求a2,a3的值 (2)求证:数列1/an是等差数列,(3)求a100
1)a(n+1)=3an/(an+3)
代入a1依次可求a2,a3.
2)a(n+1)=3an/(an+3) 两边取倒数
所以1/an+1=1/3+1/an
1/(an+1)-1/an=1/3
所以1/an是等差数列,以1/a1=2为首项,1/3为公差的等差数列.
3)求出1/a100,即得a100.
你题 是不是错了!
1.an+1=f(an)=3an / an+3
a2=3a1 / a1+3 =3/7
a3=3a2 / a2+3=9/24
2.证:∵an+1 = 3an / an+3
∴(an+1)*(an+3) = 3an
an+1*an + 3an+1 = 3an
an+1*an = 3an - 3an+1
两边同除an+1*an :1 = 3/(an...
全部展开
1.an+1=f(an)=3an / an+3
a2=3a1 / a1+3 =3/7
a3=3a2 / a2+3=9/24
2.证:∵an+1 = 3an / an+3
∴(an+1)*(an+3) = 3an
an+1*an + 3an+1 = 3an
an+1*an = 3an - 3an+1
两边同除an+1*an :1 = 3/(an+1) - 3/an
1 = 3[1/(an+1) - 1/an]
1/(an+1) - 1/an =1/3
∴数列{1/an}是以首项为2,公差为1/3的等差数列
3.∵等差数列{1/an}的通项公式=2+(n-1)*(1/3)=(n+5)/3
∴an=3/(n+5)
a100=1/35
收起
75955