Any real number in the interval [0, 1] can be represented by a decimal (not necessarily unique)
Question:
Any real number in the interval [0, 1] can be represented by a decimal (not necessarily unique) as
where di is one of the integers 0, 1, 2, 3, . . . , 9. Prove that the series on the right-hand side always converges.
Transcribed Image Text:
0.djd₂d3d4... || d₁ d₂ + 10 10² + dz d₁ + 10³ 104 +
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 60% (5 reviews)
ANSWER To prove that the series always converges we can use the comparison test We will compare the ...View the full answer
Answered By
Akash M Rathod
I have been utilized by educators and students alike to provide individualized assistance with everything from grammar and vocabulary to complex problem-solving in various academic subjects. I can provide explanations, examples, and practice exercises tailored to each student's individual needs, helping them to grasp difficult concepts and improve their skills.
My tutoring sessions are interactive and engaging, utilizing a variety of tools and resources to keep learners motivated and focused. Whether a student needs help with homework, test preparation, or simply wants to improve their skills in a particular subject area, I am equipped to provide the support and guidance they need to succeed.
0.00
0 Reviews
10+ Question Solved
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Question Posted:
Students also viewed these Mathematics questions
-
QUESTION 21 Which of the following is not a wrapper class? A. String B. Integer C. Character D. Double QUESTION 22 The conversion of an object of a wrapper class to a value of its associated...
-
The following additional information is available for the Dr. Ivan and Irene Incisor family from Chapters 1-5. Ivan's grandfather died and left a portfolio of municipal bonds. In 2012, they pay Ivan...
-
A linear dynamical system can be represented by the equations Dx / dt = A(t)x(t) + B(t)u(t), y(t) = C(t)x(t) + D(t)u(t), where A is an n n variable matrix, B is an n r variable matrix, C is an m n...
-
The Qantas Group includes a sustainability report in its annual report. What key performance indicators are included in this report? Explain the different stakeholders that would be interested in...
-
For each of the following three separate cases, use the information provided about the calendar-year 2010 operations of Kowa Company to compute the required cash flow information. Case A: Compute...
-
Marsh Limited has investigated the possibility of investing in a new machine. The following data have been extracted from the report relating to the project: Cost of machine on 1 January Year 6:...
-
Create formulas for the following in an Excel worksheet: a. Add the values of 3 and 5 to one another. b. Subtract the value of 5 from 1 O and multiply the outcome by 7. c. Average the values 5, 6, 7,...
-
At December 31, 2016, the Accounts Receivable balance of TM Manufacturer is $230,000. The Allowance for Bad Debts account has a $24,000 debit balance. TM Manufacturer prepares the following aging...
-
Before the year end adjustments, Company L's allowance for doubtful accounts balance of $7,000 DR The year-end balance for the allowance for the allowance for doubtful accounts will be based on the...
-
On July 1, 2022, Burrough Company acquired 88,000 of the outstanding shares of Carter Company for $13 per share. This acquisition gave Burrough a 25 percent ownership of Carter and allowed Burrough...
-
Which of the series converge, and which diverge? Give reasons for your answers. 00 n=1 1.3..... [2.4. (2n . (2n - 1) (2n)](3 + 1)
-
Which of the sequences {a n } converge, and which diverge? Find the limit of each convergent sequence. An (-4)" n!
-
Consider a 1.5-m-high and 2-m-wide triple pane window. The thickness of each glass layer (k = 0.80 W/m K) is 0.5 cm, and the thickness of each air space (k = 0.025 W/m K) is 1 cm. If the inner and...
-
What is the viscosity of the fluid? Why is the viscous shear stress in the fluid proportional to the rate of shear deformation, but not the amount of shear deformation?
-
Please explain the relationship between shear stress and deformation rate of Bingham fluid, pseudo-plastic fluid, swelling fluid, and Newton fluid.
-
What is the isotropy of static pressure at any point in a static fluid?
-
What is the main function of the winglet? Briefly describe the principle of pneumatics.
-
Fill in the Blank. The time taken to complete one cycle of motion is called the ________ of vibration.
-
According to market monetarists, what problems might arise from a sharp decline in Nominal GDP?
-
Respond to the ethical judgments required based on the following scenarios. Scenario 1. Assume you have collected a sample using MUS and that you have evaluated that sample to calculate a total...
-
Prove that the series obtained in Exercise 13 represents cos x for all x.
-
Prove that the series obtained in Exercise 25 represents sin x for all x.
-
Prove that the series obtained in Exercise 17 represents sinh x for all x.
-
2) a) [15 Pts.] Find the curve fit of the form y = (xAB)-1 for the following data xk 0.5 0.9 1 1.5 1.333 0.4115 0.333 0.231 b) [10 Pts.] Determine E(f) Hint: E2(f)==1lex]1/2
-
Raymond was one of the two male nurses working in an ICU in an inner-city hospital. The nurse manager always put him in charge of the ICU whenever he worked his twelve-hour shift. When Raymond was in...
-
5 . There are two elevators in Tracy Hall, side by side, so that one string tied to the left elevator goes up to a pulley and then over to the elevator on the right so when one elevator goes up , the...
Study smarter with the SolutionInn App