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Консультация № 199287
09.10.2020, 12:35
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Здравствуйте, уважаемые эксперты! Помогите пожалуйста с решением:
Обсуждение
09.10.2020, 16:45
общий
это ответ
Здравствуйте, Barsik22!
Условие : Дан числовой ряд n=1[$8734$][$8721$]{[(3·n / (n+1)]n}
Исследовать ряд на сходимость.
Решение : Кто забыл методы исследования рядов, читаем учебно-методическую статью "Ряды для чайников. Примеры решений" Ссылка .
Аннотирую : "когда нам дан ЛЮБОЙ числовой ряд, в первую очередь проверяем… стремится ли его общий член к нулю? Если не стремится - даём ответ о том, что ряд расходится".
В текущей задаче общий член an = [(3·n / (n+1)]n стремится к бесконечности, НЕ к нулю. Значит, ряд расходится.
Прилагаю скриншот с формулами.
Ответ : Ряд расходится.
Условие : Дан числовой ряд n=1[$8734$][$8721$]{[(3·n / (n+1)]n}
Исследовать ряд на сходимость.
Решение : Кто забыл методы исследования рядов, читаем учебно-методическую статью "Ряды для чайников. Примеры решений" Ссылка .
Аннотирую : "когда нам дан ЛЮБОЙ числовой ряд, в первую очередь проверяем… стремится ли его общий член к нулю? Если не стремится - даём ответ о том, что ряд расходится".
В текущей задаче общий член an = [(3·n / (n+1)]n стремится к бесконечности, НЕ к нулю. Значит, ряд расходится.
Прилагаю скриншот с формулами.
Ответ : Ряд расходится.
5
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