如图,过y轴上一点P(0,1)作平行于x轴的直线PB,分别交函数y
1=x
2(x≥0)与y
2=
![](https://math.21cnjy.com/MathMLToImage?mml=%3Cmath+xmlns%3D%22http%3A%2F%2Fwww.w3.org%2F1998%2FMath%2FMathML%22%3E%3Cmrow%3E%3Cmfrac%3E%3Cmrow%3E%3Cmsup%3E%3Cmi%3Ex%3C%2Fmi%3E%3Cmn%3E2%3C%2Fmn%3E%3C%2Fmsup%3E%3C%2Fmrow%3E%3Cmn%3E3%3C%2Fmn%3E%3C%2Fmfrac%3E%3C%2Fmrow%3E%3C%2Fmath%3E)
(x≥0)的图象于A
1 , B
1两点,过点B
1作y轴的平行线交y
1的图象于点A
2 , 再过A
2作直线A
2B
2∥x轴,交y
2的图象于点B
2 , 依次进行下去,连接A
1A
2 , B
1B
2 , A
2A
3 , B
2B
3 , …,记△A
2A
1B
1的面积为S
1 , △A
2B
1B
2的面积为S
2 , △A
3A
2B
2的面积为S
3 , △A
3B
2B
3的面积为S
4 , …则S
2016=
![](http://tikupic.21cnjy.com/e6/00/e600d9e200e7ad6a51a4ab574f715467.png)