高中数学`求救!!!!!!!

显示全部楼层 · 2008-10-5 18:06:56

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*)

千问 · 2008-10-5 18:06:56

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...