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設(shè)a>0,如圖,已知直線(xiàn)l:y=ax及曲線(xiàn)C:y=x
2,C上的點(diǎn)Q
1的橫坐標(biāo)為a
1(0<a
1<a).從C上的點(diǎn)Q
n(n≥1)作直線(xiàn)平行于x軸,交直線(xiàn)l于點(diǎn)P
n+1,再?gòu)狞c(diǎn)P
n+1作直線(xiàn)平行于y軸,交曲線(xiàn)C于點(diǎn)Q
n+1.Q
n(n=1,2,3,…)的橫坐標(biāo)構(gòu)成數(shù)列{a
n}.
(Ⅰ)試求a
n+1與a
n的關(guān)系,并求{a
n}的通項(xiàng)公式;
(Ⅱ)當(dāng)
a=1,a1≤時(shí),證明
n |
![](http://thumb.zyjl.cn/pic3/images/part/8721.png) |
k=1 |
(ak-ak+1)ak+2<;
(Ⅲ)當(dāng)a=1時(shí),證明
n |
![](http://thumb.zyjl.cn/pic3/images/part/8721.png) |
k-1 |
(ak-ak+1)ak+2<..