1正方形OA1B1C1、A1A2B2C2、A2A3B3C3、···按如图放置,其中点A1、A2、A3···在X轴的正半轴
1正方形OA1B1C1、A1A2B2C2、A2A3B3C3、···按如图放置,其中点A1、A2、A3···在X轴的正半轴上,点B1B2B3 ···在y=-x+2上,以此类推,点An的坐标为——.
2如图所示，直线1+=xy与y轴交于点1A，以1OA为边作正方形111CBOA然后延长11BC与直线1+=xy交于点2A，得到第一个梯形211AOCA；再以21AC为边作正方形2221CBAC，同样延长22BC与直线1+=xy交于点3A得到第二个梯形3212ACCA；，再以32AC为边作正方形3332CBAC，延长33BC，得到第三个梯形；……则第2个梯形3212ACCA的面积是 ；第n（n是正整数）个梯形的面积是 （用含n的式子表示）
赞 北极刺猬 幼苗
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1.
B1(b,b),b = -b + 2,b = 1
A1(1,0),OA1 = 1
直线y = 2 - x斜率-1,∠C2B2B1 = 180˚ - 135˚ = 45˚
C2B1 = C2B2 = A2B2 = A1A2 = A1B1/2 = 1/2
与此类似,A2A3 = A2B2/2 = 1/4
An的横坐标:OA1 + A1A2 + A2A3 + ...+ An-1An
= 1 + 1/2 + 1/4 + ...+ 1/2ⁿ⁻¹
= 2(1 - 1/2ⁿ)
2.
直线估计是y = x + 1
A1(0,1),C1(1,0),B1(1,1)
C1B1与直线交于点A2(1,2)
梯形上下底分别为OA1 = 1,C1A2 = 2,高OC1 = 1
直线y = x + 1斜率1,∠A2A1B1 = 45˚,A1B1 = B1A2
C1C2 = C1A2 = 2,C2A3 = 2C2B2 = 4
梯形下底分别为2,4,高2
与此类似,第n个梯形上底Cn-1Bn-1 = 2ⁿ⁻¹,下底CnAn+1 = 2ⁿ,高Cn-1Cn = n
面积 = (1/2)(2ⁿ⁻¹ + 2ⁿ)*n
= n(2ⁿ⁻¹ + 2ⁿ)/2
B1(b,b),b = -b + 2,b = 1
A1(1,0),OA1 = 1
直线y = 2 - x斜率-1,∠C2B2B1 = 180˚ - 135˚ = 45˚
C2B1 = C2B2 = A2B2 = A1A2 = A1B1/2 = 1/2
与此类似,A2A3 = A2B2/2 = 1/4
An的横坐标:OA1 + A1A2 + A2A3 + ...+ An-1An
= 1 + 1/2 + 1/4 + ...+ 1/2ⁿ⁻¹
= 2(1 - 1/2ⁿ)
2.
直线估计是y = x + 1
A1(0,1),C1(1,0),B1(1,1)
C1B1与直线交于点A2(1,2)
梯形上下底分别为OA1 = 1,C1A2 = 2,高OC1 = 1
直线y = x + 1斜率1,∠A2A1B1 = 45˚,A1B1 = B1A2
C1C2 = C1A2 = 2,C2A3 = 2C2B2 = 4
梯形下底分别为2,4,高2
与此类似,第n个梯形上底Cn-1Bn-1 = 2ⁿ⁻¹,下底CnAn+1 = 2ⁿ,高Cn-1Cn = n
面积 = (1/2)(2ⁿ⁻¹ + 2ⁿ)*n
= n(2ⁿ⁻¹ + 2ⁿ)/2
1年前
4
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