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Консультация № 196651
11.10.2019, 20:08
0.00 руб.
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Здравствуйте, уважаемые эксперты! Прошу вас ответить на следующий вопрос:
сверху +бесконечность n=1
сверху +бесконечность n=1
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Обсуждение
12.10.2019, 21:57
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naks1mok Найти сумму ряда
С какой точностью?
Об авторе:
Facta loquuntur.
Facta loquuntur.
12.10.2019, 23:13
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А само задание из какого источника взято? Чувствуется, что уровень задания выше того, который присущ заданиям, например, для студентов машиностроительных специальностей вузов.
Об авторе:
Facta loquuntur.
Facta loquuntur.
12.10.2019, 23:19
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Учебно-методическое пособие от Шинтемировой Гульжихан Бейсембаевны
12.10.2019, 23:27
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А в виде, доступном для загрузки на компьютер, это пособие у Вас есть?
Об авторе:
Facta loquuntur.
Facta loquuntur.
12.10.2019, 23:32
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А по какой специальности Вы получаете высшее образование, если не секрет?
Об авторе:
Facta loquuntur.
Facta loquuntur.
12.10.2019, 23:34
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Это знакомой помогаю у неё специальность :"Информационные системы"
12.10.2019, 23:36
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Хорошо. Я попробую разобраться с этой задачей. Если получится решить её, то оформлю ответ. 
Об авторе:
Facta loquuntur.
Facta loquuntur.
14.10.2019, 06:54
общий
это ответ
Здравствуйте, naks1mok!
Разложим общий член ряда в сумму простых дробей:
an = 8/(16n2-8n-15) = 1/(4n-5) - 1/(4n+3) = 1/(4n-5) - 1/(4(n+2)-5);
Обозначим
bn = 1/(4n-5), тогда an = bn - bn+2.
SN = [$8721$]an = [$8721$](bn - bn+2) = [$8721$]bn - [$8721$]'bn = b1 + b2 - bN+1 - bN+2.
где [$8721$] - сумма от n=1 до N, [$8721$]' - сумма от n=3 до N+2.
В пределе N[$8594$][$8734$] плучим сумму ряда
S = b1 + b2= 1/(4-5) + 1/(4*2-5) = -1 +1/3 = -2/3.
Разложим общий член ряда в сумму простых дробей:
an = 8/(16n2-8n-15) = 1/(4n-5) - 1/(4n+3) = 1/(4n-5) - 1/(4(n+2)-5);
Обозначим
bn = 1/(4n-5), тогда an = bn - bn+2.
SN = [$8721$]an = [$8721$](bn - bn+2) = [$8721$]bn - [$8721$]'bn = b1 + b2 - bN+1 - bN+2.
где [$8721$] - сумма от n=1 до N, [$8721$]' - сумма от n=3 до N+2.
В пределе N[$8594$][$8734$] плучим сумму ряда
S = b1 + b2= 1/(4-5) + 1/(4*2-5) = -1 +1/3 = -2/3.
5
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