0.3 +0.03 +0.003 +0.0003 + ... (a) Express the series in the form M8 n=1 an (b) Does this series converge or diverge? Justify your response with the appropriate series test. (c) What is the sum of this infinite series? (Give your answer as a fully-reduced fraction.)

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.1: Sequences And Series
Problem 9ECP: For the series i=1510i find (a) the fourth partial sum and (b) the sum. Notice in Example 9(b) that...
icon
Related questions
Question

Please solve the calc 2 problem (all parts use calc 2 concepts only) 

 

3.
Consider the infinite series below.
0.3 + 0.03 +0.003 +0.0003 + ··
(a) Express the series in the form
∞
Σ
n=1
an
(b) Does this series converge or diverge? Justify your response with the appropriate series test.
(c) What is the sum of this infinite series? (Give your answer as a fully-reduced fraction.)
Transcribed Image Text:3. Consider the infinite series below. 0.3 + 0.03 +0.003 +0.0003 + ·· (a) Express the series in the form ∞ Σ n=1 an (b) Does this series converge or diverge? Justify your response with the appropriate series test. (c) What is the sum of this infinite series? (Give your answer as a fully-reduced fraction.)
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

Blurred answer
Recommended textbooks for you
College Algebra
College Algebra
Algebra
ISBN:
9781337282291
Author:
Ron Larson
Publisher:
Cengage Learning
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
College Algebra
College Algebra
Algebra
ISBN:
9781305115545
Author:
James Stewart, Lothar Redlin, Saleem Watson
Publisher:
Cengage Learning
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage