The meaning of the decimal representation of a number 0.d1d2d3 . . . (where the digit di

Question:

The meaning of the decimal representation of a number 0.d1d2d3 . . . (where the digit di is one of the numbers 0, 1, 2 . . . 9) is that

Show that this series always converges.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus Early Transcendentals

ISBN: 978-0538497909

7th edition

Authors: James Stewart

See More Books

Question Posted: Jul 10, 2010 01:44 AM

See More Questions

The meaning of the decimal representation of a number 0.d1d2d3 (where the digit d1 is one of the numbers 0, 1, 2,...,9) is that 0.d1d2d3...= d1/10 d2/102 + d3/103 + d4/104 + ... Show that this series...
The meaning of the decimal representation of a number 0.d 1 d 2 d 3 . . . (where the digit d i is one of the numbers 0, 1, 2, . . . , 9) is that di d2 0.d, d2dzd4 ... dz d4 10 102 103 104
One digit in each of these identification numbers of a postal money order is smudged. Can you recover the smudged digit, indicated by a Q, in each of these numbers? a) 493212Q0688 b) 850Q9103858 c)...
GoFast Corp. wishes to renovate the property so that he can sell it at a higher price.The after-tax cash flow over next year up to RM320,000 if the property was renovated.The renovation cost is...
The Food and Drug Administration sets a Food Defect Action Level (FDAL) for the various foreign substances that inevitably end up in the food we eat and liquids we drink. For example, the FDAL level...
In Exercise 3.101 on page 108, the price of a certain commodity (in dollars) and its total sales (in 10,000 units) were denoted by P and S. Use the joint density given in that exercise and the...
Why may it be argued that the concept of the manager is socially constructed rather than real? LO6
Why do better decision regarding the purchasing and managing of goods for sale frequently cause dramatic percentage increases in net income?
A bank has a basket of three-year loans with a value of $ 5 million that pay annual interest of $200,000 per annum. Interest payments are conducted every year but the total principals of the loans...
(4) A production process at Kenneth Day Manufacturing is shown in the figure below. The drilling operation occurs separately from, and simultaneously with, sawing and sanding, which are independent...
Show that the series ( 1)n 1bn, where bn = 1/n if n is odd and bn = 1/ n2if n is even, is divergent. Why does the Alternating Series Test not apply?
Suppose an and bn are series with positive terms and bn is known to be convergent. (a) If an > bn for all n, what can you say about an? Why? (b) If an < bn for all n, what can you say about an? Why?
For the elementary process N2O5(g) NO2(g) + NO3(g) the activation energy (Ea) and overall (E are 154 kJ/mol and 136 kJ/mol, respectively. (a) Sketch the energy profile for this reaction, and label...
The transmitted energy expands out into space as it propagates at 3 GHz between the transmitter and the receiver over 30 km distance. Calculate the free space loss using a suitable formula and any...
What is the company featured in this episode of Undercover Boss? List 3 good professional activities that the CEO/president learned about their company by going undercover? List areas of the...
Assume there is a national lottery in the winning ticket is worth $10 million one winning ticket will be selected if there are 225 million tickets sold. What is the chance that a buyer of one ticket...
Description: Reference: Basu Thakur. (2015). PostcolonialTheory and Avatar (pp. 85-150,157-172). Bloomsbury PublishingUSAPre-Peer Paper Review for the Postcolonial Application Paper 1: Collecting...
NOT ASKING THE ACTUAL SHEAR STRESS. Please READ! Derive the shear stress distributed equation over the cross-section. Derive the equation and plot. 15 15 30 15 15 120 -90 20 0.5 m 72 kN 20 20 40 40...
2. For each of the following, evaluate I Is curl F . nda. (a) 8 is the "bottomless" surface in the upper half space z 2 bounded by y = x2, Z = 1 - y, n is the outward-pointing normal, and F(x,y,z) =...
Briefly describe the following types of group life insurance plans: a. Group term life insurance b. Group accidental death and dismemberment insurance (AD&D) c. Group universal life insurance d....
How can an unexpected fall in exchange rates injure the financial health of a nations banks?
Calculate the value of the multiple integral. D y dA, where D is the region in the first quadrant bounded by the parabolas x = y 2 and x = 8 y 2
(a) Find a function f such that F = f (b) Use part (a) to evaluate C F dr along the given curve C. F(x, y) = (2x, 4y), C is the arc of the parabola x = y 2 from (4, 2) to (1, 1).
(a) Set up an iterated integral in polar coordinates for the volume of the solid under the surface and above the region D. (b) Evaluate the iterated integral to find the volume of the solid. z= x? +...
Eye Deal Optometry leased vision - testing equipment from Insight Machines on January 1 , 2 0 2 4 . Insight Machines manufactured the equipment at a cost of $ 2 0 0 , 0 0 0 and lists a cash selling...
help! ee all photos + Add to o e D C N X Edit & Create Share Table of Contents No sales to an individual customer accounted for more than 10% of revenue during any of the last three fiscal years. Net...
Business law A person may have the liability of a partner even though no partnership exists True False

The meaning of the decimal representation of a number 0.d1d2d3 . . . (where the digit di

Question:

dz d, 10 104 da 0.dıdzdsda.. 10 10?

Step by Step Answer:

dn 10n 0d1d2d3 Since 9 10n fo...View the full answer

Calculus Early Transcendentals

Students also viewed these Calculus questions