Question

Use the Limit Comparison Test to determine whether the series converges. $$ \sum_{k=1}^{\infty} \frac{k^4 + 1}{k^5 - 9} $$ The Limit Comparison Test with $$ \sum_{k=1}^{\infty} $$ shows that the series

Name: use the limit comparison test to determine whether the series converges sumk1infty frack4 1k5 9 the limit comparison test with sumk1infty shows that the series 59136
Uploaded: 2020-05-16T14:07:19-08:00
Duration: 2 min 7 s
Channel: Linh Vu
Description: use the limit comparison test to determine whether the series converges sumk1infty frack4 1k5 9 the limit comparison test with sumk1infty shows that the series 59136

          Use the Limit Comparison Test to determine whether the series converges.
$$ \sum_{k=1}^{\infty} \frac{k^4 + 1}{k^5 - 9} $$
The Limit Comparison Test with $$ \sum_{k=1}^{\infty} $$ shows that the series

$use the limit comparison test to determine whether the series converges sumk1infty frack4 1k5 9 the limit comparison test with sumk1infty shows that the series 59136$

Added by Raul C.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Linh Vu

05/16/2020

Step 1

The series is: $$ \sum_{k=1}^{\infty} \frac{k^4 + 1}{k^5 - 9} $$ Let $a_k = \frac{k^4 + 1}{k^5 - 9}$. For large $k$, the dominant term in the numerator is $k^4$ and the dominant term in the denominator is $k^5$. So, $a_k$ behaves like $\frac{k^4}{k^5} = Show more…

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Use the Limit Comparison Test to determine whether the series converges. $$ \sum_{k=1}^{\infty} \frac{k^4 + 1}{k^5 - 9} $$ The Limit Comparison Test with $$ \sum_{k=1}^{\infty} $$ shows that the series