高中数学`求救!!!!!!!

来源:百度知道 编辑:UC知道 时间:2024/06/05 16:57:41
f(x)=0.25x^2+0.5x+0.25

求证:1/f(1)+1/f(2)+....+1/f(n)>2n/(n+2) (n∈N*)

证:f(x)=0.25x^2+0.5x+0.25 =(0.5x+0.5)^2

1/f(x)=4/(x+1)^2>4/(x+1)*(x+2)=4[1/(x+1)-1/(x+2)]

1/f(1)+1/f(2)+....+1/f(n)>4(1/2-1/3)+4(1/3-1/4)+4(1/4-1/5)....+
4[1/(x+1)-1/(x+2)](中间项都约掉,剩下首尾2项)=4[1/2-1/(x+2)]=2-4/(x+2)=2x/(x+2)
啊,不好意思,写成x了,把x改成n