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Консультация № 185689
27.03.2012, 19:29
103.21 руб.
0
2
2
Уважаемые эксперты! Пожалуйста, ответьте на вопрос:
https://rfpro.ru/upload/7820 - задание здесь
https://rfpro.ru/upload/7820 - задание здесь
Обсуждение
27.03.2012, 19:39
общий
это ответ
Здравствуйте, Aleksandrkib!
1a
По радикальному признаку Коши ряд расходится
1б
Не выполняется необходимое условие сходимости ряда.
1в
Члены исходного ряда мешьше членов сходящегося ряда Дирихле, следовательно, по первому признаку сравнения ряд сходится.
2
-11<x<1 - в этом интервале ряд сходится абсолютно.
Исследуем граничные точки:
Знакочередующийся ряд сходится по признаку Лейбница, так как предел абсолютных значений его членов равен 0.
Это сходящийся ряд Дирихле.
Ответ: Область сходимости ряда: [-11;1]
1a
По радикальному признаку Коши ряд расходится
1б
Не выполняется необходимое условие сходимости ряда.
1в
Члены исходного ряда мешьше членов сходящегося ряда Дирихле, следовательно, по первому признаку сравнения ряд сходится.
2
-11<x<1 - в этом интервале ряд сходится абсолютно.
Исследуем граничные точки:
Знакочередующийся ряд сходится по признаку Лейбница, так как предел абсолютных значений его членов равен 0.
Это сходящийся ряд Дирихле.
Ответ: Область сходимости ряда: [-11;1]
27.03.2012, 19:45
общий
это ответ
Здравствуйте, Aleksandrkib!
1 б)
Необходимым условием сходимости ряда является стремление к 0 его членов.
Член ряда не стремится к 0, следовательно, ряд расходится.
Если x+5=6, получаем сходящийся ряд
Если x+5=-6, получаем абсолютно сходящийся ряд
Если |x+5|<6, ряд сходится, так как ограничен сверху рядом q^n
Если |x+5|<6, ряд расходится, так как ограничен
Область сходимости ряда [-11;1]
1 б)
Необходимым условием сходимости ряда является стремление к 0 его членов.
Член ряда не стремится к 0, следовательно, ряд расходится.
Если x+5=6, получаем сходящийся ряд
Если x+5=-6, получаем абсолютно сходящийся ряд
Если |x+5|<6, ряд сходится, так как ограничен сверху рядом q^n
Если |x+5|<6, ряд расходится, так как ограничен
Область сходимости ряда [-11;1]
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