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Консультация № 198481
07.05.2020, 18:09
0.00 руб.
0
2
1
Здравствуйте! Прошу помощи в следующем вопросе:
Исследовать сходимость числового ряда
Исследовать сходимость числового ряда
Обсуждение
15.05.2020, 18:05
общий
это ответ
Здравствуйте, Svet_Vitalievna!
Воспользуемся признаком сравнения: если начиная с некоторого n a[sub]n[/sub][$8804$]b[sub]n[/sub], и ряд [$8721$]b[sub]n[/sub] сходится, то ряд [$8721$]a[sub]n[/sub] также сходится, если же a[sub]n[/sub][$8805$]b[sub]n[/sub], и ряд [$8721$]b[sub]n[/sub] расходится, то ряд [$8721$]a[sub]n[/sub] также расходится. В данном случае имеем
при всех n > 7, и так как ряд
расходится (как и любой ряд вида
при a[$8804$]1), то и ряд
также расходится.
Воспользуемся признаком сравнения: если начиная с некоторого n a[sub]n[/sub][$8804$]b[sub]n[/sub], и ряд [$8721$]b[sub]n[/sub] сходится, то ряд [$8721$]a[sub]n[/sub] также сходится, если же a[sub]n[/sub][$8805$]b[sub]n[/sub], и ряд [$8721$]b[sub]n[/sub] расходится, то ряд [$8721$]a[sub]n[/sub] также расходится. В данном случае имеем
при всех n > 7, и так как ряд
расходится (как и любой ряд вида
при a[$8804$]1), то и ряд
также расходится.
5
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