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По-моему, всё-таки не каждая. Например, последняя стремится к 5, да и предыдущие тоже. Я, кстати, посчитал этот предел численно (на компьютере) - получилось примерно 2.75. Так что Ваше решение, скорее всего, неверно.
где x[sub]1[/sub] = 1/n, x[sub]2[/sub] = 2/n,... x[sub]i[/sub] = i/n,... x[sub]n[/sub] = 1 - точки, делящие отрезок [0,1] на n равных частей длиной [$916$]x[sub]i[/sub] = 1/n. Сумма вида
называется интегральной суммой функции f(x) на отрезке [x[sub]0[/sub], x[sub]n[/sub]] и для неё по определению
В нашем случае f(x) = ln(1+4x), [$916$]x[sub]i[/sub] [$8801$] 1/n, x[sub]0[/sub] = 0, x[sub]n[/sub] = 1 и
откуда
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