Question 1: Crazy series (50 points)

In this session, you need to implement the crazy series method. In the crazy series, you will be given a starting number. Then, you need to times 2 for each number until the number is greater than 100. After the number is greater than 100, you need to divide 3 until we reach the number is less than 5. Note that the input number must be greater than 0, and you are not allowed to use loop here.

For example,

crazySeries(10) should return ArrayList [10.0, 20.0, 40.0, 80.0, 160.0, 53.333333333333336, 17.77777777777778, 5.9259259259259265, 1.9753086419753088]

crazySeries(5) should return ArrayList [5.0, 10.0, 20.0, 40.0, 80.0, 160.0, 53.333333333333336, 17.77777777777778, 5.9259259259259265, 1.9753086419753088]

crazySeries(1) should return ArrayList [1.0, 2.0, 4.0, 8.0, 16.0, 32.0, 64.0, 128.0, 42.666666666666664, 14.222222222222221, 4.7407407407407405]

Question 2: Ben number (50 points)

Ben had difficulty coming out with an assignment question, then he created an odd number called Ben number, which is the sum of a Ben series. Let x be the starting number and y be the bout number, in the Ben series, the x should double the value when it is an even number. In contrast, the number should be subtracted by 1 when x is an odd number. Both x and y should be greater than 0.

Example of a Ben series,

Assume the x = 3, and y = 5, then the series should be

[3, 2, 4, 8,16]. Then the Ben number should be 33 because of 3+2+4+18+16.

Thus, given the method benNumber(m,n), for all m, n > 0

benNumber(2,5) should return 62 because 2+4+8+16+32 = 62

benNumber(3,8) should return 257 because 3+2+4+8+16+32+64+128 = 257

benNumber(1,1) should return 1