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Я понял интуитивно, что данная последовательность не ограничена, но как это строго доказать, так и не понял. Попробовал составить неравенство , где c - некоторое положительное число. На этом мои продвижения по задаче закончились.
По-моему, Вы были правы, когда сообщили: Цитата: pavel.simpavel
Я понял интуитивно, что данная последовательность не ограничена, ...
Как я понимаю, для доказательства того, что заданная последовательность не ограничена, нужно доказать, что каким большим ни было бы положительное число найдётся такое натуральное число что будет выполняться неравенство Это неравенство равносильно такому: Поскольку в силу неограниченности множества натуральных чисел всегда найдутся натуральные числа и такие, что и то неравенство будет тем более выполняться, если выполняется неравенство Последнее неравенство будет выполняться, если взять А это и значит, что последовательность не ограничена.
Об авторе:
Facta loquuntur.
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на ограниченность.
, где c - некоторое положительное число. На этом мои продвижения по задаче закончились.
pavel.simpavel 
найдётся такое натуральное число 
что будет выполняться неравенство 
Это неравенство равносильно такому: 
Поскольку в силу неограниченности множества натуральных чисел всегда найдутся натуральные числа 
и 
такие, что 
и 
то неравенство 
будет тем более выполняться, если выполняется неравенство 
Последнее неравенство будет выполняться, если взять 
А это и значит, что последовательность 
не ограничена.