18-20. Evaluating geometric series two ways Evaluate each geomet- ric series two ways. a. Find the nth partial sum S, of the series and evaluate lim S b. Evaluate the series using Theorem 10.7. k=0 THEOREM 10.7 Geometric Series a Let a + 0 and r be real numbers. If |r| < 1, then ark If |r| > 1, k=0 then the series diverges. Diverges rs-1 Converges -1

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
18-20. Evaluating geometric series two ways Evaluate each geomet-
ric series two ways.
a. Find the nth partial sum S, of the series and evaluate lim S
b. Evaluate the series using Theorem 10.7.
k=0
Transcribed Image Text:18-20. Evaluating geometric series two ways Evaluate each geomet- ric series two ways. a. Find the nth partial sum S, of the series and evaluate lim S b. Evaluate the series using Theorem 10.7. k=0
THEOREM 10.7 Geometric Series
a
Let a + 0 and r be real numbers. If |r| < 1, then ark
If |r| > 1,
k=0
then the series diverges.
Diverges
rs-1
Converges
-1<r<1
Diverges
Transcribed Image Text:THEOREM 10.7 Geometric Series a Let a + 0 and r be real numbers. If |r| < 1, then ark If |r| > 1, k=0 then the series diverges. Diverges rs-1 Converges -1<r<1 Diverges
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 3 steps

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