Question

\sum_(n=1)^(\infty ) (n)/(\sqrt(n^(5)+n+1)) using ONLY either ratio or root test does the series converge or diverge? $\sum_{n=1}^{\infty} \frac{n}{\sqrt{n^5 + n + 1}}$

Name: sumn1infty nsqrtn5n1 using only either ratio or root test does the series converge or diverge sumn1infty fracnsqrtn5 n 1 56318
Uploaded: 2021-10-03T15:25:16-08:00
Duration: 57 s
Channel: Nick Johnson
Description: sumn1infty nsqrtn5n1 using only either ratio or root test does the series converge or diverge sumn1infty fracnsqrtn5 n 1 56318

          \sum_(n=1)^(\infty ) (n)/(\sqrt(n^(5)+n+1)) using ONLY either ratio or root test does the series converge or diverge?
$\sum_{n=1}^{\infty} \frac{n}{\sqrt{n^5 + n + 1}}$

$sumn1infty nsqrtn5n1 using only either ratio or root test does the series converge or diverge sumn1infty fracnsqrtn5 n 1 56318$

Added by Javier A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Nick Johnson

10/03/2021

Step 1

We can compare this series with the series $\sum_{n=1}^{\infty} \frac{n}{\sqrt{n^5}} = \sum_{n=1}^{\infty} \frac{n}{n^{5/2}} = \sum_{n=1}^{\infty} \frac{1}{n^{3/2}}$. Show more…

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\sum_(n=1)^(\infty ) (n)/(\sqrt(n^(5)+n+1)) using ONLY either ratio or root test does the series converge or diverge? $\sum_{n=1}^{\infty} \frac{n}{\sqrt{n^5 + n + 1}}$