Show that if Deduce that Show that if r n a (1 r) 2 as n Hence sum the infinite series T a 2ar 3ar 4ar nar 1 then (1r)T, a ar ar ar nar...

Show that if Deduce that Show that if |r| n a/(1 r) 2 as n

Question:

Show that if

T= a + 2ar + 3ar + 4ar+...+ nar-1 then (1r)T, = a +ar+ar+...+ar"- - nar

Deduce that

T = a(1-r") (1-r) nar" 1-r

Show that if |r| n → a/(1 – r)² as n → ∞. Hence sum the infinite series

- 1+ 3/3 + 1/3 + 27 5 + + 81 + k 3k-1 +.

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

Step by Step Answer:

Related Book For book-img-for-question

Modern Engineering Mathematics

ISBN: 9781292253497

6th Edition

Authors: Glyn James

See More Books

Question Posted: Jan 13, 2024 09:04 AM

See More Questions

1. Find values for S and R that satisfy S = 0.3R and 0.2 (100 + S) = R. Show that these solutions give the same stipend and rent as found by summing the infinite series. 2. Suppose that instead of a...
If an annuity makes an infinite series of equal payments at the end of the interest periods, it is called a perpetuity. If a lump sum investment of An is needed to result in n periodic payments of R...
Which of the following statements is correct? a. The left side of a T-account is the credit side. b. Debits decrease asset and expense accounts and increase liability, equity, and revenue accounts....
The following post-closing trial balance was prepared for Speedy Prints, Inc., but some balances were entered in the wrong column. Prepare a corrected post-closing trial balance. Assume all accounts...
During the 4.0 min a 5.0 A current is set up in a wire, how many (a) Coulombs and (b) Electrons pass through any cross section across the wire's width?
On August 31, Baginski and Company receives its bank statement ( shown below). The company deposits its receipts in the bank and makes all payments by check. The debit memo for $ 95 is for an NSF...
Give a scenario where the partitions rule applies. LO5
The following information was taken from the 2008 and 2009 Form 10-Ks for Dell, Inc. Required a. Explain whether each line of information in the table above would best be described as being primarily...
Record the transaction for January using a purchase journal page 56 WOO Vy Work Correct Record the transactions for January, using a purchases journal, page 56. If an amount box does not require an...
For each of the following series find the sum of the first N terms, and, by letting N , show that the infinite series converges and state its sum. 2 2 2 5-7 (a) 13 + + + ... (b) + + + + 2+... 1 (c)...
Decide which of the following geometric series are convergent. (a) 2 + 2 + 2 3 (b) 4-2+1 9 + 2 27 1 2 (c) 10 + 11 + 21 10 2 + + + 3k (-1)* 4 2k +...+10()*+.. ... +...+ 1331 100 +... 25 125 (d) 1 - 1...
Why do diverse teams focus more on data than homogeneous teams?
In the global discourse on healthcare, the United States and England stand out as two contrasting models, each providing a distinct approach to addressing the challenges of cost , access, and...
2.A. Using the quotes below, answer the following questions. Exchange rate Bid Ask In New York, USD/EUR 1.2267 1.2875 In London, USD/GBP 1.6555 1.7334 2.A1. Calculate the EUR/GBP cross exchange...
Question 43 Part B Q1ii 20 points Save A a) A property is currently leased for $100,000 p.a. with fully recoverable outgoings. The lease has 3 years to run on the current (fixed) rent. The market...
Define HIPPA? What is the purpose of HIPPA? What are the 4 main rules of HIPPA?
Accounting for Inventories" Please respond to the following: As a Financial Accountant,determine the best type of income statement a retailer should use.Defend your suggestion. Analyze inventory...
The probability that the total on the two die is 4 or more. (To use the law of total probability, find the probability that the score is 4 or more if the first die gives a 1, if the first die gives a...
Record the following selected transactions for March in a two-column journal, identifying each entry by letter: (a) Received $10,000 from Shirley Knowles, owner. (b) Purchased equipment for $35,000,...
The three lowest energy levels for atomic carbon (C) have the following energies and degeneracies: Determine the electronic contribution to C V for atomic C at 100. K. Level (n) Energy (cm)...
Carbon dioxide has attracted much recent interest as a greenhouse gas. Determine the vibrational contribution to C V for CO 2 , where 1 = 2349 cm -1 , 2 = 667 cm -1 (doubly degenerate), and 3 =...
Determine the vibrational contribution to C V for HCN, where 1 = 2041 cm -1 , 2 = 712 cm -1 (doubly degenerate), and 3 = 3369 cm -1 at T = 298, 500, and 1000.K.
A government bond matures in 30 years, makes semi-annual coupon payments of 6.0% ($120 per year) and offers a yield of 3.7% annually compounded. Assume face value is $1,000. Three years later the...
Your objective is: 1. Carry out a life insurance needs analysis, for each one of them (show your calculations) [30 Marks] 2. Refer to the case and the insurance plan quotes. Would you recommend...
TufStuff, Incorporated, sells a wide range of drums, bins, boxes, and other containers that are used in the chemical industry. One of the company s products is a heavy - duty corrosion - resistant...

Show that if Deduce that Show that if |r| n a/(1 r) 2 as n

Question:

T= a + 2ar + 3ar + 4ar+...+ nar-1 then (1r)T, = a +ar+ar+...+ar"- - nar

Step by Step Answer:

In a 2ar 3ar 4ar In ar 2ar ...View the full answer

Modern Engineering Mathematics

Students also viewed these Sciences questions