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Консультация № 187628
21.11.2013, 19:01
96.47 руб.
21.11.2013, 19:22
0
4
4
Уважаемые эксперты! Помогите пожалуйста решить данные задания:
Обсуждение
21.11.2013, 19:46
общий
это ответ
Здравствуйте, Андрей!
№7
Так как предел на бесконечности меньше 1, то ряд сходится по признаку Даламбера.
№7
Так как предел на бесконечности меньше 1, то ряд сходится по признаку Даламбера.
5
Спасибо!
21.11.2013, 21:45
общий
это ответ
Здравствуйте, Андрей!
№ 1. В числителе и знаменателе общего члена ряда находятся многочлены. Старшая степень числителя равна
Старшая степень знаменателя равна 
Из старшей степени знаменателя вычитаем старшую степень числителя: 
Сравним заданный ряд с расходящимся рядом 
Используем предельный признак сравнения:
Получено конечное число, не равное нулю. Следовательно, заданный ряд расходится вместе с рядом
С уважением.
№ 1. В числителе и знаменателе общего члена ряда находятся многочлены. Старшая степень числителя равна
Старшая степень знаменателя равна Из старшей степени знаменателя вычитаем старшую степень числителя: Сравним заданный ряд с расходящимся рядом Используем предельный признак сравнения:Получено конечное число, не равное нулю. Следовательно, заданный ряд расходится вместе с рядом
С уважением.
5
Спасибо!
Об авторе:
Facta loquuntur.
Facta loquuntur.
22.11.2013, 15:30
общий
это ответ
Здравствуйте, Андрей!
№8
Следовательно,
Итак,
Согласно признаку Коши данный ряд сходится.
№8
Следовательно,
Итак,
Согласно признаку Коши данный ряд сходится.
5
Спасибо!
22.11.2013, 16:10
общий
это ответ
Здравствуйте, Андрей!
N9
Вводим f(x)=-8/xln9x
В соответствии с интегральным признаком Коши иследуем сходимость интеграла
I=[$8747$]2+[$8734$]f(x)dx=-8[$8747$]2+[$8734$]dx/xln9x
Делая замену t=ln x, получаем
I=-8[$8747$]ln 2+[$8734$]dt/t9=(1/t8)|ln 2+[$8734$]=-1/ln82
Так как интеграл сходится, то ряд также сходится.
N9
Вводим f(x)=-8/xln9x
В соответствии с интегральным признаком Коши иследуем сходимость интеграла
I=[$8747$]2+[$8734$]f(x)dx=-8[$8747$]2+[$8734$]dx/xln9x
Делая замену t=ln x, получаем
I=-8[$8747$]ln 2+[$8734$]dt/t9=(1/t8)|ln 2+[$8734$]=-1/ln82
Так как интеграл сходится, то ряд также сходится.
5
Спасибо!
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