As shown in the figure, divide a square with an area of 1 into two rectangles with an area of 1 / 2, then divide the rectangle with an area of 1 / 2 into two squares with an area of 1 / 4, and then divide the square with an area of 1 / 4 into two rectangles with an area of 1 / 8. In this way, try to use the law revealed by the figure to calculate: 1 / 2 + 1 / 4 + 1 / 8 + 1 / 16 + 1 / 32 + 1 / 64 + 1 / 128 + 1 / 256 = What is the area of a small rectangle obtained by the eighth equal division?

It can be seen from the figure that after every bisection, there will always be two rectangles with the smallest area left. And the area of a small rectangle obtained after the nth bisection is 1 / (the nth power of 2), and no matter it is added to the nth power of 1 / 2, there will be one remaining 1 / (the nth power of 2), then 1 / 2 + 1 / 4 = 1-1 / 41 / 2 + 1 / 4 + 1 / 8 = 1-1 / 8 So, 1 / 2 + 1

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1. Divide a square with an area of 1 into two rectangles with an area of half Divide a square with an area of 1 into two rectangles with an area of 1 / 2, then divide the rectangle with an area of 1 / 2 into two rectangles with an area of 1 / 4, and then divide the rectangle with an area of 1 / 4 into two rectangles with an area of 1 / 8. In this way, try to use the law revealed by the graph to calculate: 1 / 2 + 1 / 4 + 1 / 8 + 1 / 6 + 1 / 32 + 1 / 128 =?
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