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Консультация № 175625
Обсуждение
Неизвестный
26.12.2009, 18:30
общий
это ответ
Здравствуйте, Андрей Владимирович Маракулин.
Используем предельный признак сравнения . Пусть другой ряд с общим членом V(n)=1/(n^3) . Тогда
Lim[U(n)/V(n)]=Lim[(n^3)/(((2n+1)^3)-1)]={ делим числитель и наменатель на (n^3) } = 1/8 = 0,125 .
Это конечное вполне определённое число .
Ряд с общим членом V(n)=1/(n^3) сходится как обобщённый гармонический ряд . Исходя из проведённого выше расчёта приходм к выводу что исходный ряд с общим членом U(n) также сходится по предельному признаку сравнения .
Используем предельный признак сравнения . Пусть другой ряд с общим членом V(n)=1/(n^3) . Тогда
Lim[U(n)/V(n)]=Lim[(n^3)/(((2n+1)^3)-1)]={ делим числитель и наменатель на (n^3) } = 1/8 = 0,125 .
Это конечное вполне определённое число .
Ряд с общим членом V(n)=1/(n^3) сходится как обобщённый гармонический ряд . Исходя из проведённого выше расчёта приходм к выводу что исходный ряд с общим членом U(n) также сходится по предельному признаку сравнения .
5
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