Answered: 1 Let an n > 3. n vln n +00 Use the…

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1 Let an n > 3. n vln n +00 Use the Integral Test to determine if the series An converges or diverges. n=3

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.3: Geometric Sequences

Problem 50E

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Question

Use the Integral Test (Let f(x) be equal to a function that is corresponding to a_n) to determine if the given series converges or diverges.

Please show first that the integral test can be applied considering that f is a function that is continuous, positive-valued, and decreasing on [1, +∞), and suppose that f(n) = an for all n ∈ N.

1
n > 3.
Let an
nvlnn
+oo
Use the Integral Test to determine if the series >
An converges or diverges.
n=3

With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.

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