Accordingly, when y takes-1, x can take 3,7, 1 1, 4k+3, and their probabilities should be added up, and the same is true for other reasons.

And here is the sum of infinite series, which is the knowledge of the university. To be honest, it's a little out of line. To put it simply, take P(Y= 1) as an example and write it as:

Here, the above formula can be obtained by the summation formula of equal ratio series, where k is a natural number, infinite. In the end, it will get bigger and bigger, and the corresponding 4 th power k of 2 will get bigger and bigger. You should have learned the image of 1/x as follows:

1/x image

You will find that when x becomes infinite, the y value of the image of 1/x gets closer and closer to the coordinate axis of y=0. This is called the concept of limit in mathematics, and I remember it was mentioned in junior high school and senior high school. Here, when the geometric series, the corresponding k becomes infinite, a quarter of k of 2 will eventually become 0. The points below are similar. The bigger k is, the closer it is to 0. The corresponding is as follows:

Of course, what I wrote here is problematic according to the standard, but you can calculate it in this way. The others are similar.

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