Рассмотрим равенство 1 = 2/(3 –1). Если единицу в знаменателе заменим на 2/(3 – 1), то получим: 1 = 2/(3 – 2/(3 – 1)). Повторив эту операцию по отношению к новой единице, стоящей в знаменателе, и поступая далее подобным образом, мы построим бесконечную цепную дробь:
1=2/(3-2/(3-2/(3-2/(3-... .
С другой стороны, 2 = 2 / (3 - 2), так что:
2 = 2/(3-2) = 2/(3-2/(3-2)) = 2/(3-2/(3-2/(3-2/(3-... .
Построенные дроби равны! Значит, равны и числа, из которых они получены, то есть 1 = 2.
1=2/(3-2/(3-2/(3-2/(3-... .
С другой стороны, 2 = 2 / (3 - 2), так что:
2 = 2/(3-2) = 2/(3-2/(3-2)) = 2/(3-2/(3-2/(3-2/(3-... .
Построенные дроби равны! Значит, равны и числа, из которых они получены, то есть 1 = 2.
Consider the equality 1 = 2 / (3 –1). If the unit in the denominator is replaced by 2 / (3 - 1), then we get: 1 = 2 / (3 - 2 / (3 - 1)). Repeating this operation in relation to the new unit standing in the denominator, and proceeding further in a similar way, we will construct an infinite continued fraction:
1 = 2 / (3-2 / (3-2 / (3-2 / (3 -...
On the other hand, 2 = 2 / (3 - 2), so that:
2 = 2 / (3-2) = 2 / (3-2 / (3-2)) = 2 / (3-2 / (3-2 / (3-2 / (3 -....
Fractions constructed are equal! Hence, the numbers from which they are derived are also equal, that is, 1 = 2.
1 = 2 / (3-2 / (3-2 / (3-2 / (3 -...
On the other hand, 2 = 2 / (3 - 2), so that:
2 = 2 / (3-2) = 2 / (3-2 / (3-2)) = 2 / (3-2 / (3-2 / (3-2 / (3 -....
Fractions constructed are equal! Hence, the numbers from which they are derived are also equal, that is, 1 = 2.
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