已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)
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![已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)](/uploads/image/z/5556250-10-0.jpg?t=%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%EF%BC%883x%2B2%EF%BC%89%2F%EF%BC%88x%2B2%EF%BC%89%2C%EF%BC%881%EF%BC%89%E8%8B%A5%E6%95%B0%E5%88%97%EF%B9%9Ban%EF%B9%9C%2C%EF%B9%9Bbn%EF%B9%9C%E6%BB%A1%E8%B6%B3a1%3D1%2F2%2Ca%28n%2B1%29%EF%BC%9C%E6%B3%A8%EF%BC%9A%E4%B8%8B%E8%84%9A%E6%A0%87%EF%BC%9Ef%3D%EF%BC%88an%EF%BC%89%E5%B7%B2%E7%9F%A5%E5%87%BD%E6%95%B0f%EF%BC%88x%EF%BC%89%3D%EF%BC%883x%2B2%EF%BC%89%2F%EF%BC%88x%2B2%EF%BC%89%2C%EF%BC%881%EF%BC%89%E8%8B%A5%E6%95%B0%E5%88%97%EF%B9%9Ban%EF%B9%9C%2C%EF%B9%9Bbn%EF%B9%9C%E6%BB%A1%E8%B6%B3a1%3D1%2F2%2Ca%28n%2B1%29%EF%BC%9C%E6%B3%A8%EF%BC%9A%E4%B8%8B%E8%84%9A%E6%A0%87%EF%BC%9Ef%3D%EF%BC%88an%EF%BC%89)
已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)
已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)
已知函数f(x)=(3x+2)/(x+2),
(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an),bn=1/﹙an+1﹚(n≧1),数列﹛bn﹜的通项公式
(2)记sn=b1+b2+…+bn,若1/sn≤m恒成立,求m的最小值
已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)已知函数f(x)=(3x+2)/(x+2),(1)若数列﹛an﹜,﹛bn﹜满足a1=1/2,a(n+1)<注:下脚标>f=(an)
(1)
b1=1/(a1+1)=1/(1/2+1)=2/3
b(n+1)=1/(f(an)+1)=(an+2)/(4an+4)=1/4(1+1/(an+1))=1/4(1+bn)
==>
bn=1/4+1/4b(n-1)
=1/4+1/16+1/16b(n-2)
=1/4+1/16+1/64+1/64b(n-3)
=.
=1/4+(1/4)^2+(1/4)^3+...+(1/4)^(n-1)+(1/4)^(n-1)b1
=1/4(1+(1/4)^(n-1))/(1-1/4)+(1/4)^(n-1)b1
=1/4(1-(1/4)^(n-1))/(1-1/4)+(1/4)^(n-1)b1
=1/4-(1/4)^(n-1)/3+2(1/4)^(n-1)/3
=1/4+(1/4)^(n-1)/3
(2)
sn=n/4+(4/3)(1-(1/4)^n)/(1-1/4)
=n/4+(16/9)(1-(1/4)^n)
=n/4-4^(2-n)/9+16/9
sn随n的递增而递增.s1=b1=2/3>0.因此sn≥2/3
所以1/sn≤3/2.对于任意k≤3/2有 1/s1≥k.
因此m=3/2
具体思路大概是这样,
huhu .