Pascal's triangle is a triangle in which there are ones at the top and along the sides, and each number is equal to the sum of the two numbers located above it. What is the sum of all the numbers in the 12th row?

Question

Вопрос:

Pascal's triangle is a triangle in which there are ones at the top and along the sides, and each number is equal to the sum of the two numbers located above it. What is the sum of all the numbers in the 12th row?

Ответ:

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Accepted Answer

Сумма чисел в n-й строке треугольника Паскаля равна 2 в степени (n-1). Следовательно, сумма чисел в 12-й строке равна 2 в степени (12-1), то есть 2 в 11 степени.

Вычислим 2 в 11 степени:

$$2^{11} = 2048$$

Ответ: 2048