Determine whether the series ∑n=1^∞ (3)/(n^3 + 4) converges or diverges by comparing it to the s

Name: Determine whether the series ∑n=1^∞ (3)/(n^3 + 4) converges or diverges by comparing it to the series ∑n=1^∞ (1)/(n^3). The series converges. The series diverges. The test is inconclusive.
Uploaded: 2023-05-05T14:17:17-08:00
Duration: 4 min 32 s
Channel: Ivan Kochetkov
Description: Determine whether the series ∑n=1^∞ (3)/(n^3 + 4) converges or diverges by comparing it to the series ∑n=1^∞ (1)/(n^3). The series converges. The series diverges. The test is inconclusive.

Question

Determine whether the series \sum_{n=1}^{\infty} \frac{3}{n^3 + 4} converges or diverges by comparing it to the series \sum_{n=1}^{\infty} \frac{1}{n^3}. \newline The series converges. \newline The series diverges. \newline The test is inconclusive.

          Determine whether the series \sum_{n=1}^{\infty} \frac{3}{n^3 + 4} converges or diverges by comparing it to the series \sum_{n=1}^{\infty} \frac{1}{n^3}. \newline The series converges. \newline The series diverges. \newline The test is inconclusive.

Determine whether the series ∑n=1^∞ (3)/(n^3 + 4) converges or diverges by comparing it to the series ∑n=1^∞ (1)/(n^3). The series converges. The series diverges. The test is inconclusive.

Added by James C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Ivan Kochetkov

05/05/2023

Step 1

Step 1: We will compare the given series \sum_(n=1)^(∞) (3)/(n^(3)+4) to the series \sum_(n=1)^(∞) (1)/(n^(3)). Show more…

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Determine whether the series sum_(n=1)^(infty ) (3)/(n^(3)+4) converges or diverges by comparing it to the series sum_(n=1)^(infty ) (1)/(n^(3)). The series converges. The series diverges. The test is inconclusive. Determine whether the series 3 2 converges or diverges by n=1 n3+4 1 comparing it to the series IM: n3 OThe series converges The series diverges OThe test is inconclusive