Question

Объяснить идею последовательности 1,10,1011,1011000,10110001111 (Можно по подробнее) самому понятному ответу поставлю отметку „Лучший ответ“ (100 баллов)

Answer 1

Начинаем с последовательности, состоящей из одной единицы: "1". Поочередно приписываем справа нули и единицы, каждый раз увеличивая количество приписанных цифр на одну. В первый раз приписывается цифра "0", во второй – цифры "11", в третий – цифры "000", и так далее.

1 + 0 = 10

10 + 11 = 1011

1011 + 000 = 1011000

1011000 + 1111 = 10110001111

Можно продолжить и дальше:

10110001111 + 00000 = 1011000111100000

1011000111100000 + 111111 = 1011000111100000111111

...

Answer 2

Ответ:

Пошаговое объяснение:

Пусть n - номер элемента последовательности, тогда

при n = 1 имеем  $x_1 = 1$

Если n нечетное, то

                                      $x_n = x_{n-1} * 10^{n-1} + \cfrac{10^{n-1}-1}{9}$

Если n четное, то

                                        $x_n = x_{n-1} * 10^{n-1}$

Получаем:

$n = 1: x_1 = 1\\\\n = 2: x_2 = x_1 * 10^{2-1} = x_1 * 10 = 10\\\\n = 3: x_3 = x_2 * 10^{3-1} + \cfrac{10^{3-1}-1}{9} = x_2 * 10^2 + 11 = 1011\\\\n = 4: x_4 = x_3 * 10^3 = 1011000\\\\n = 5: x_5 = x_4 * 10^4 + \cfrac{10^4-1}{9} = 10110001111\\\\n = 6: x_6 = x_5 * 10^5 = 1011000111100000\\\dots$

Answer 3

Idea behind the sequence 1, 10, 1011, 1011000, 10110001111

The sequence 1, 10, 1011, 1011000, 10110001111 follows a specific pattern. Let's break it down step by step to understand the idea behind this sequence.

1. The first term is 1. 2. The second term is formed by concatenating the binary representation of the decimal number 2, which is 10. 3. The third term is formed by concatenating the binary representation of the decimal number 3, which is 11, to the second term. So, the third term becomes 1011. 4. The fourth term is formed by concatenating the binary representation of the decimal number 4, which is 100, to the third term. So, the fourth term becomes 1011000. 5. The fifth term is formed by concatenating the binary representation of the decimal number 5, which is 101, to the fourth term. So, the fifth term becomes 10110001111.

In general, each term in the sequence is formed by concatenating the binary representation of the decimal number corresponding to its position in the sequence to the previous term.

Explanation of the pattern

The pattern in this sequence is based on the concept of concatenating binary representations of decimal numbers. Let's analyze it further:

- The first term is simply 1, which is the binary representation of the decimal number 1. - The second term is formed by concatenating the binary representation of the decimal number 2 to the first term. The binary representation of 2 is 10. - The third term is formed by concatenating the binary representation of the decimal number 3 to the second term. The binary representation of 3 is 11. - The fourth term is formed by concatenating the binary representation of the decimal number 4 to the third term. The binary representation of 4 is 100. - The fifth term is formed by concatenating the binary representation of the decimal number 5 to the fourth term. The binary representation of 5 is 101.

This pattern continues for subsequent terms in the sequence.

Conclusion

In summary, the sequence 1, 10, 1011, 1011000, 10110001111 follows a pattern where each term is formed by concatenating the binary representation of the decimal number corresponding to its position in the sequence to the previous term. This pattern demonstrates the concept of concatenating binary representations of decimal numbers to form a sequence.