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Консультация № 192276
01.01.2018, 11:35
0.00 руб.
0
7
1
Здравствуйте! Прошу помощи в следующем вопросе:
Известно, что последовательности (Xn) , (Yn) сходятся.
Верно ли, что последовательность (3x^2n+yn) всегда сходится?
Подскажите, пожалуйста, от чего отталкиваться. Свое начало в приложении.
Известно, что последовательности (Xn) , (Yn) сходятся.
Верно ли, что последовательность (3x^2n+yn) всегда сходится?
Подскажите, пожалуйста, от чего отталкиваться. Свое начало в приложении.
Обсуждение
01.01.2018, 13:10
общий
Адресаты:
IIISergeyIII Подскажите, пожалуйста, от чего отталкиваться.
"Отталкиваться" нужно от того, что сумма (разность) двух сходящихся последовательностей есть сходящаяся последовательность, предел которой равен сумме (разности) пределов рассматриваемых последовательностей; произведение двух сходящихся последовательностей есть сходящаяся последовательность, предел которой равен произведению пределов рассматриваемых последовательностей.
Отсюда сразу следует ответ на вопрос задания.
Об авторе:
Facta loquuntur.
Facta loquuntur.
01.01.2018, 13:31
общий
Адресаты:
В целом правильно. Используется ещё то, что постоянный множитель можно вынести за знак предела.
А если Вас попросят вычислить, чему равен предел рассматриваемой последовательности, то что Вы напишете?
А если Вас попросят вычислить, чему равен предел рассматриваемой последовательности, то что Вы напишете?
Об авторе:
Facta loquuntur.
Facta loquuntur.
01.01.2018, 14:03
общий
это ответ
Здравствуйте, IIISergeyIII!
Как мы с Вами установили в мини-форуме консультации, рассмотренная последовательность сходится. Записанное Вами решение в целом правильное. Вместо ссылки на номер теоремы лучше указать её название или даже кратко изложить вывод теоремы. Предложения лучше поменять местами. Тогда получится примерно так: "Так как
сходится и 
сходится, то сходятся и 
".
Как мы с Вами установили в мини-форуме консультации, рассмотренная последовательность сходится. Записанное Вами решение в целом правильное. Вместо ссылки на номер теоремы лучше указать её название или даже кратко изложить вывод теоремы. Предложения лучше поменять местами. Тогда получится примерно так: "Так как
сходится и сходится, то сходятся и ".
Об авторе:
Facta loquuntur.
Facta loquuntur.
01.01.2018, 17:22
общий
Адресаты:
IIISergeyIII 3 * (предел Xn) ^2 + предел(Yn)
Правильно.
Об авторе:
Facta loquuntur.
Facta loquuntur.
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