If sum_{n=1}^{infinity} a_n diverges and 0 <= a_n <= b_n for all n, which of the following statements must be true? A sum_{n=1}^{infinity} (-1)^n a_n converges. B sum_{n=1}^{infinity} (-1)^n b_n converges. C sum_{n=1}^{infinity} (-1)^n b_n diverges. D sum_{n=1}^{infinity} b_n converges. E sum_{n=1}^{infinity} b_n diverges.
Added by David P.
Close
Step 1
We are told that the sequence \(a_n\) diverges, \(0 < a_n < b_n\) for all \(n\), and we need to determine the truth about several statements regarding convergence or divergence of sequences involving \(a_n\) and \(b_n\). Show more…
Show all steps
Your feedback will help us improve your experience
Madhur L and 95 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
Consider the series sum_{n=1}^{infinity} a_n and sum_{n=1}^{infinity} b_n, where a_n > 0 and b_n > 0 for n >= 1. If sum_{n=1}^{infinity} a_n converges, which of the following must be true? A If a_n <= b_n, then sum_{n=1}^{infinity} b_n converges. B If a_n <= b_n, then sum_{n=1}^{infinity} b_n diverges. C If b_n <= a_n, then sum_{n=1}^{infinity} b_n converges. D If b_n <= a_n, then sum_{n=1}^{infinity} b_n diverges. E If b_n <= a_n, then the behavior of sum_{n=1}^{infinity} b_n cannot be determined from the information given.
Tuli H.
Suppose lim an = 0 and an+1 > an > 0 for all n > 1. Which of the following statements must be true? A. ̲(-1)^n an converges for n = 1 to infinity. B. ̲an converges for n = 1 to infinity. C. ̲(1/an) converges for n = 1 to infinity. D. ̲an diverges for n = 1 to infinity.
Adi S.
Which of the sequences $\left\{a_{n}\right\}$ converge, and which diverge? Find the limit of each convergent sequence. $$ a_{n}=\left(\frac{1}{n}\right)^{1 /(\ln n)} $$
Infinite Sequences and Series
Sequences
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