Which of the following is true? O If an infinite series An converges then the sequence of its partial sums converges to 0: lim az = 0 OIf lim a, = 0 n00 then an converges. An infinite sum of positive numbers always diverges to infinity. OIf lim an #0 n00 then an n=1 diverges.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
icon
Related questions
Question
Which of the following is true?
If an infinite series
an
n=0
converges then the sequence of its partial sums converges to 0:
lim
az = 0
k-1
OIf
lim an = 0
then
an
n=1
converges.
An infinite sum of positive numbers always diverges to infinity.
O If
lim an #0
then
n=1
diverges.
Transcribed Image Text:Which of the following is true? If an infinite series an n=0 converges then the sequence of its partial sums converges to 0: lim az = 0 k-1 OIf lim an = 0 then an n=1 converges. An infinite sum of positive numbers always diverges to infinity. O If lim an #0 then n=1 diverges.
Expert Solution
steps

Step by step

Solved in 2 steps with 1 images

Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning