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Консультация № 202953
30.05.2022, 19:46
0.00 руб.
1
1
1
Здравствуйте! У меня возникли сложности с таким вопросом:
Вычислить приближенно с точностью до 10^-3
Вычислить приближенно с точностью до 10^-3
Прикрепленные файлы:
Обсуждение
01.06.2022, 22:23
общий
это ответ
Здравствуйте, Julius Caesar!
Имеем
Воспользуемся следующим разложением в степенной ряд
при
Тогда получим, что
Для ряда, который содержится во внутренней паре скобок выражения (1), имеем
Ряд (2) можно записать и в общем виде так:
причём, поскольку
постольку мажорирующим для ряда (3) является ряд
образованный членами бесконечной геометрической прогрессии с первым членом
и знаменателем 
где 
Сумма этой прогрессии
а её первый остаток --
Стало быть, и первые остатки рядов (4), (3) и (2) не превосходят
а первый остаток ряда (1) не превосходит 
Поэтому с точностью до 
можно принять, что
Имеем
Воспользуемся следующим разложением в степенной ряд
при
Тогда получим, чтоДля ряда, который содержится во внутренней паре скобок выражения (1), имеем
Ряд (2) можно записать и в общем виде так:
причём, поскольку
постольку мажорирующим для ряда (3) является рядобразованный членами бесконечной геометрической прогрессии с первым членом
и знаменателем где Сумма этой прогрессииа её первый остаток --
Стало быть, и первые остатки рядов (4), (3) и (2) не превосходят
а первый остаток ряда (1) не превосходит Поэтому с точностью до можно принять, что
Об авторе:
Facta loquuntur.
Facta loquuntur.
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