Question

Use the Integral Test to determine the convergence or divergence of the series, where k is a positive integer. ∞ nk − 1nk + c n = 1 ∞ xk − 1xk + c dx = 1 convergesdiverges

Name: use the integral test to determine the convergence or divergence of the series where k is a positive integer nk 1nk c n 1 xk 1xk c dx 1 convergesdiverges 84135
Uploaded: 2022-02-09T05:58:50-08:00
Duration: 3 min 18 s
Channel: Ma. Theresa Alin
Description: use the integral test to determine the convergence or divergence of the series where k is a positive integer nk 1nk c n 1 xk 1xk c dx 1 convergesdiverges 84135

          Use the Integral Test to determine the convergence or divergence of the series, where k is a positive integer.
∞
nk − 1nk + c
n = 1
∞
xk − 1xk + c
 dx =
1
convergesdiverges

Added by Antonio A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ma. Theresa Alin

02/09/2022

Step 1

The series given is: \[ \sum_{n=1}^\infty \frac{n^{k-1}}{n^k + c} \] where \(k\) is a positive integer and \(c\) is a constant. Define the function: \[ f(x) = \frac{x^{k-1}}{x^k + c} \] for \(x \geq 1\). Show more…

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Use the Integral Test to determine the convergence or divergence of the series, where k is a positive integer. ∞ nk − 1nk + c n = 1 ∞ xk − 1xk + c dx = 1 convergesdiverges