(b) Let x = 0.9999.... Do you think that x <1 or x = 1? (c) Sum a geometric series to find the value of x. (d) How many decimal representations does the number 1 have? Write them all down. (e) Which numbers have more than one decimal representation?

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 30E
icon
Related questions
Topic Video
Question

 Recall that the decimal representation of a number is a sequence of digits with one separator (decimal point), which separates the integer part of a number from its fractional part. 

(b) Let x = 0.9999 .. .. Do you think that x <1 or x = 1?
(c) Sum a geometric series to find the value of x.
(d) How many decimal representations does the number 1 have? Write them all down.
(e) Which numbers have more than one decimal representation?
Transcribed Image Text:(b) Let x = 0.9999 .. .. Do you think that x <1 or x = 1? (c) Sum a geometric series to find the value of x. (d) How many decimal representations does the number 1 have? Write them all down. (e) Which numbers have more than one decimal representation?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps

Blurred answer
Knowledge Booster
Sequence
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.
Recommended textbooks for you
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill
College Algebra
College Algebra
Algebra
ISBN:
9781938168383
Author:
Jay Abramson
Publisher:
OpenStax
College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
Algebra
ISBN:
9781305652231
Author:
R. David Gustafson, Jeff Hughes
Publisher:
Cengage Learning