Explanation If { a n } is a sequence of real numbers. Then the expression S n = a 1 + a 2 + ... + a n = ∑ k = 1 n a k is termed as sequence of n th partial sum, i.e., the sum of first n terms of a sequence and S = lim n → ∞ S n = a 1 + a 2 + ... + a n + ... = ∑ n = 1 ∞ a n is known as sum of infinite terms of sequence termed as infinite series. The given series is termed as positive term series if in the series S = a 1 + a 2 + ... + a n + ... = ∑ n = 1 ∞ a n , a n > 0 ∀ n ∈ N . An infinite series S = lim n → ∞ S n = a 1 + a 2 + ... + a n + ... = ∑ n = 1 ∞ a n is said to be convergent or divergent if its n th partial sum S n = a 1 + a 2 + ... + a n = ∑ k = 1 n a k is convergent to finite value or divergent to infinity. Necessary and sufficient condition for convergence Necessary and sufficient condition that infinite series S = ∑ n = 1 ∞ a n is said to be convergent if lim n → ∞ a n = 0 . Suppose a n ≥ 0 ∀ n ∈ N , then S = ∑ n = 1 ∞ a n is said to be convergentif and only if S n = a 1 + a 2 + ... + a n = ∑ k = 1 n a k is bounded above...

4th Edition

ISBN: 9781319323394

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Videos

Question

Chapter 11.4, Problem 35E

To determine

Acounterexample in which the alternating series test is not applicable when the n^thterm tends to zero but is not assumed to be decreasing.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11.4, Problem 34E

Chapter 11.4, Problem 36E

Students have asked these similar questions

Decide whether each limit exists. If a limit exists, estimate its value. 11. (a) lim f(x) x-3 f(x) ↑ 4 3- 2+ (b) lim f(x) x―0 -2 0 X 1234

Determine whether the lines L₁ (t) = (-2,3, −1)t + (0,2,-3) and L2 p(s) = (2, −3, 1)s + (-10, 17, -8) intersect. If they do, find the point of intersection.

Convert the line given by the parametric equations y(t) Enter the symmetric equations in alphabetic order. (x(t) = -4+6t = 3-t (z(t) = 5-7t to symmetric equations.

Chapter 11 Solutions

CALCULUS W/SAPLING ACCESS >IC<

Ch. 11.1 - Prob. 1PQ Ch. 11.1 - Prob. 2PQ Ch. 11.1 - Prob. 3PQ Ch. 11.1 - Prob. 4PQ Ch. 11.1 - Prob. 5PQ Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E Ch. 11.1 - Prob. 3E Ch. 11.1 - Prob. 4E Ch. 11.1 - Prob. 5E

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.

Acounterexample in which the alternating series test is not applicable when the n th term tends to zero but is not assumed to be decreasing.

Solution Summary: The author explains that the alternating series test is not applicable for the given infinite series.

Videos

Acounterexample in which the alternating series test is not applicable when the n^thterm tends to zero but is not assumed to be decreasing.

Want to see the full answer?

Chapter 11 Solutions

Acounterexample in which the alternating series test is not applicable when the n th term tends to zero but is not assumed to be decreasing.

Solution Summary: The author explains that the alternating series test is not applicable for the given infinite series.

Videos

Acounterexample in which the alternating series test is not applicable when the nthterm tends to zero but is not assumed to be decreasing.

Want to see the full answer?

Chapter 11 Solutions

Acounterexample in which the alternating series test is not applicable when the n^thterm tends to zero but is not assumed to be decreasing.