Question

4. Use the Root Test to determine whether the positive series $\sum_{n=1}^{\infty} \left(\frac{4n^3}{5n^3+2}\right)^n$ converges or diverges.

Name: 4. Use the Root Test to determine whether the positive series ∑n=1^∞((4n^3)/(5n^3+2))^n converges or diverges.
Uploaded: 2022-08-05T20:53:38-08:00
Duration: 2 min 26 s
Channel: Zhumagali Shomanov
Description: 4. Use the Root Test to determine whether the positive series ∑n=1^∞((4n^3)/(5n^3+2))^n converges or diverges.

          4. Use the Root Test to determine whether the positive series $\sum_{n=1}^{\infty} \left(\frac{4n^3}{5n^3+2}\right)^n$ converges or diverges.

Added by Derrick G.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

08/05/2022

Step 1

Let a_n = ((4n^3)/(5n^3+2))^n We need to find lim (n→∞) (|a_n|)^(1/n) = lim (n→∞) ((4n^3)/(5n^3+2)) = lim (n→∞) (4/(5 + 2/n^3)) = 4/5 Show more…

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Use the Root Test to determine whether the positive series sum_(n=1)^(infty ) ((4n^(3))/(5n^(3)+2))^(n) converges or diverges. 4n3 4. Use the Root Test to determine whether the positive series 5n3+2 n=1 verges. converges or di-