Question

Use the limit comparison test to determine whether $\sum_{n=7}^{\infty} a_n = \sum_{n=7}^{\infty} \frac{5n^3 - 6n^2 + 7}{9 + 4n^4}$ converges or diverges. (a) Choose a series $\sum_{n=7}^{\infty} b_n$ with terms of the form $b_n = \frac{1}{n^p}$ and apply the limit comparison test. Write your answer as a fully simplified fraction. For $n \ge 7$, $\lim_{n \to \infty} \frac{a_n}{b_n} = \lim_{n \to \infty}$ (b) Evaluate the limit in the previous part. Enter $\infty$ as infinity and $-\infty$ as -infinity. If the limit does not exist, enter DNE. $\lim_{n \to \infty} \frac{a_n}{b_n} =$ (c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive?

Name: use the limit comparison test to determine whether sumn7infty an sumn7infty frac5n3 6n2 79 4n4 converges or diverges a choose a series sumn7infty bn with terms of the form bn frac1np a 29336
Uploaded: 2023-03-28T01:20:54-08:00
Duration: 4 min 51 s
Channel: Zhumagali Shomanov
Description: use the limit comparison test to determine whether sumn7infty an sumn7infty frac5n3 6n2 79 4n4 converges or diverges a choose a series sumn7infty bn with terms of the form bn frac1np a 29336

          Use the limit comparison test to determine whether $\sum_{n=7}^{\infty} a_n = \sum_{n=7}^{\infty} \frac{5n^3 - 6n^2 + 7}{9 + 4n^4}$ converges or diverges.

(a) Choose a series $\sum_{n=7}^{\infty} b_n$ with terms of the form $b_n = \frac{1}{n^p}$ and apply the limit comparison test. Write your answer as a fully simplified fraction. For $n \ge 7$,

$\lim_{n \to \infty} \frac{a_n}{b_n} = \lim_{n \to \infty}$

(b) Evaluate the limit in the previous part. Enter $\infty$ as infinity and $-\infty$ as -infinity. If the limit does not exist, enter DNE.

$\lim_{n \to \infty} \frac{a_n}{b_n} =$

(c) By the limit comparison test, does the series converge, diverge, or is the test inconclusive?

$use the limit comparison test to determine whether sumn7infty an sumn7infty frac5n3 6n2 79 4n4 converges or diverges a choose a series sumn7infty bn with terms of the form bn frac1np a 29336$

Added by Andrew A.

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