Although the topic is long, it is not difficult to find the law. You should clear your mind and don't be confused. This topic studies the application and design of drawing and the change rules of graphics. You should look at the topic information and understand the method of segmentation. The problem of finding the law often appears. See the answer/exercise/math /798885. So don't be frightened by such a long topic. Generally, it is not particularly difficult.

Query 1: Calculate1/2+1/2+1/23+...+1/2n.

Divide the area of the square by 1, where the area of the shaded part is1/2;

In the second division, the area of the blank part in the last division is divided into two parts, and the sum of the areas of the shadow part is1/2+1/22;

The third division, continue to divide the area of the blank part in the last division into two, …

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For the nth partition, divide the blank part in the last partition into two halves. The sum of all shaded areas is1/2+1/22+1/23+...+1/2n, and the area of the last blank part is 65438+.

According to the nth partition graph, the equation can be obtained:1/2+1/2 2+1/2 3+…+1/2n =1-kloc-0//2n.