Explanation Given: The series is ∑ k = 1 ∞ 1 k 3 − k + 1 . Result used: (1) “Let ∑ a k and ∑ b k are the series with positive terms and let lim n → ∞ a n b n = L , where L is a finite number. (i) If 0 < L < ∞ , then ∑ a k and ∑ b k either both series converge or both diverge.” (ii) If L = 0 and ∑ b k converges, then ∑ a k converges. (iii) If L = ∞ and ∑ b k diverges, then ∑ a k diverges”. (2) The p -series ∑ k = 1 ∞ 1 k p is convergent if p > 1 . Calculation: Consider k 3 + 1 < k 3 + k for all k ≤ 1 . k 3 − k + 1 < k 3 1 k 3 < 1 k 3 − k + 1 1 k 3 < 1 k 3 − k + 1 ∑ k = 1 ∞ 1 k 3 − k + 1 > ∑ k = 1 ∞ 1 k 3 Consider the series ∑ k = 1 ∞ b k = ∑ k = 1 ∞ 1 k 3 , which must be smaller than ∑ k = 1 ∞ a k = ∑ k = 1 ∞ 1 k 3 − k + 1

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 10.5, Problem 47E

To determine

Whether the series ∑k=1∞1k3−k+1 converges or diverges.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 10.5, Problem 46E

Chapter 10.5, Problem 48E

Students have asked these similar questions

↑ Use an appropriate test to determine whether the following series converges. IM8 Σ 1 k=2 (k-1)4 Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.) 00 A. The series diverges by the Integral Test. The value of S 1 Oc. The series diverges. It is a p-series with p = D. The series converges. It is a p-series with p = 2 (x-1) OB. The series diverges by the Divergence Test. The value of lim 1 k→∞ (k-1) dx is OE. The series converges by the Divergence Test. The value of lim 4 1 k→∞ (k-1) is 4 is COD layer/player.aspx?cultureld=&theme=math&style=highered&disableStandbyIndicator=true&assignmentHandles Locale=true# This question: 1 pointe

Using the Direct Comparison Test or the Limit Comparison Test determine if the series converges or diverges.

Binomial seriesa. Find the first four nonzero terms of the binomial series centered at 0 for the given function.b. Use the first four terms of the series to approximate the given quantity.

Chapter 10 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. 10.1 - Find a10 for the sequence {1, 4, 7, 10, ...} using...Ch. 10.1 - Prob. 2QC Ch. 10.1 - Prob. 3QC Ch. 10.1 - Do the series k=11 and k=1k converge or diverge?Ch. 10.1 - Prob. 5QC Ch. 10.1 - Prob. 1E Ch. 10.1 - Prob. 2E Ch. 10.1 - Prob. 3E Ch. 10.1 - Find two different explicit formulas for the...Ch. 10.1 - Find two different explicit formulas for the...

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

Whether the series ∑ k = 1 ∞ 1 k 3 − k + 1 converges or diverges.

Solution Summary: The author analyzes whether the series displaystyle 'underset' is convergent or divergent.

Videos

Whether the series ∑k=1∞1k3−k+1 converges or diverges.

Want to see the full answer?

Chapter 10 Solutions