[ sum_{n=1}^{infty} frac{cos (n)}{4^{n}} ] converges by the Direct Comparison Test diverges by the Direct Comparison Test diverges by the Alternating Series Test converges by the Alternating Series Test
Added by Rh77
Close
Step 1
First, we know that the absolute value of cos(n) is always less than or equal to 1. Show more…
Show all steps
Your feedback will help us improve your experience
Andrew Noble and 91 other Calculus 2 / BC 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
Use the limit comparison test to determine whether the series converges or diverges. $\sum_{n=1}^{\infty}\left(1-\cos \frac{1}{n}\right),$ by comparing to $\sum_{n=1}^{\infty} \frac{1}{n^{2}}$
Sequences and Series
Tests for Convergence
Use the limit comparison test to determine whether the series converges or diverges. $\sum_{n=1}^{\infty} \frac{n}{\cos n+e^{n}}$
Use the Direct Comparison Test to determine whether each series converges or diverges. $$\sum_{n=1}^{\infty} \frac{n-1}{n^{4}+2}$$
Infinite Sequences and Series
Comparison Tests
Recommended Textbooks
Calculus: Early Transcendentals
Thomas Calculus
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD