9. Use the Integral Test to determine whether the series converges or diverges. $\sum_{n=1}^{\infty} \frac{1}{(3n-1)^4}$
Added by Jose N.
Close
Step 1
Step 1: The Integral Test states that if f(x) is a continuous, positive, and decreasing function for x ≥ 1, and a_n = f(n), then the series ∑ a_n converges if and only if the improper integral ∫ f(x) dx from 1 to ∞ converges. Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 57 other Calculus 1 / AB educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Confirm that the integral test is applicable and use it to determine whether the series converges.
Adi S.
Use the Integral Test to determine whether the series convergent or divergent.
Madhur L.
Confirm that the Integral Test can be applied to the series. Then use the Integral Test to determine the convergence or divergence of the series. $$\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+\frac{1}{9}+\frac{1}{11}+\cdots$$
Infinite Series
The Integral Test and p-Series
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD