Determine if the series $\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{\sqrt{n^2}}$ converges absolutely, converges conditionally, or diverges. (5 pts)

Name: Determine if the series ∑n=1^∞((-1)^n-1)/(√(n^2)) converges absolutely, converges conditionally, or diverges. (5 pts)
Uploaded: 2023-05-05T15:26:44-08:00
Duration: 1 min 42 s
Channel: Sam Stansfield
Description: Determine if the series ∑n=1^∞((-1)^n-1)/(√(n^2)) converges absolutely, converges conditionally, or diverges. (5 pts)

          Determine if the series $\sum_{n=1}^{\infty} \frac{(-1)^{n-1}}{\sqrt{n^2}}$ converges absolutely, converges conditionally, or diverges. (5 pts)

Added by Luis S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Sam Stansfield

05/05/2023

Step 1

To determine if the series converges absolutely, we need to consider the absolute value of each term in the series. The absolute value of ((-1)^(n-1))/(\root(5)(n^(2))) is 1/(n^(2/5)). We can use the p-series test to determine if the series \sum_(n=1)^(∞) Show more…

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Determine if the series sum_(n=1)^(infty ) ((-1)^(n-1))/( oot(5)(n^(2))) converges absolutely, converges conditionally, or diverges. (-1-1 Determine if the series converges absolutely,converges conditionally,or n=1 2/n2 diverges. (5 pts)