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题目

MAT136H5 S 2025 - All Sections 5.3 preparation check

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Read Theorem 5.9: Integral Test from the textbook Links to an external site. .    Suppose you are given a series ∑ 𝑛 = 1 ∞ 𝑎 𝑛  and that you have already found a function 𝑓 ( 𝑥 ) such that 𝑓 ( 𝑛 ) = 𝑎 𝑛 for all integers 𝑛 ≥ 𝑁   for some positive integer 𝑁 . If you wanted to use the Integral Test to find out if the series converges or diverges, which of the following would you need to do? (Select all that apply.)

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When applying the Integral Test, we need to ensure certain conditions about the associated function f(x) and the series terms a_n hold true, so a careful check of each statement is in order. Option 1: Evaluate the integral ∫_N^∞ f(x) dx (or determine another way to assess convergence). This is central to the Integral Test. One uses the improper integral of f(x) from N to infinity to compare its convergence with that of......Login to view full explanation

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