Show that if n is a positive integer, then k 4 n(3n 7) k 1 k (k 1 )(k 2) 2(n 1 )(n 2)...

We use induction If n 1 then the lefthand side has just one term na ...

Show that if n is a positive integer, then k +4 n(3n 7) k= 1 k (k

Question:

Show that if n is a positive integer, then

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

Step by Step Answer:

Related Book For book-img-for-question

Discrete Mathematics and Its Applications

ISBN: 978-0073383095

7th edition

Authors: Kenneth H. Rosen

See More Books

Question Posted: May 02, 2016 12:31 PM

See More Questions

Prove that if n is a positive integer, then n is odd if and only if 5n + 6 is odd.
(Gamma Function) Let Î(n) = This integral converges by Problems 51 and 52. Show each of the following (note that the gamma function is defined for every positive real number n): (a) Î(1)...
If n is a positive integer, show that
Diagonalize the matrices, if possible. The eigenvalues are as follows: (11) = 1, 2, 3; (12) = 1, 4; (13) = 5, 1; (14) = 3, 4; (15) = 3, 1; (16) = 2, 1. 3 4 6 1
Inter Global Industries is a diversified corporation with separate operating divisions. Each divisions performance is evaluated on the basis of profit and return on investment. The Air Comfort...
Sketch the output waveform resulting in Fig. 10.69. 0.1 F 200 k0 V +15 V FIG. 10.69 Problem 10
Using the results of Problem 3.1, show numerically that the square of the simple correlation coefficient between the observed values $y_{i}$ and the fitted values $\hat{y}_{i}$ equals $R^{2}$. Data...
a. Create a data flow diagram of the current system. b. Create a system flowchart of the existing system. c. Analyze the internal control weaknesses in the system. Model your response according to...
Moody Corporation uses a job-order costing system with a plantwide predetermined overhead rate based on machine-hours. At the beginning of the year, the company made the following estimates:...
Real Value Corporation (the Company), is a public company (and an SEC registrant) that creates augmented reality technology. The Companys primary source of revenue is currently from universities that...
Use mathematical induction to prove that 64 divides 32n+2 + 56n + 55 for every positive integer n.
Suppose that f (x) = ex and g(x) = xex. Use mathematical induction together with the product rule and the fact that f'(x) = ex to prove that g(n)(x) = (x + n)ex whenever n is a positive integer.
Given the following cost and activity observations for Smithson Company's utilities, use the high-low method to calculate Smithson's fixed costs per month. Round variable cost per unit to two decimal...
Compared to using the FIFO method to account for inventory, during periods of rising prices, a company using the LIFO method is most likely to report higher: A. net income. B. cost of sales. C....
Intangible assets with finite useful lives mostly differ from intangible assets with infinite useful lives with respect to accounting treatment of: A. revaluation. B. impairment. C. amortization.
Inventory cost is least likely to include: A. production-related storage costs. B. costs incurred as a result of normal waste of materials. C. transportation costs of shipping inventory to customers.
Jordans response about the effect of Alphas revaluation is most likely correct with respect to the impact on its: A. return on equity. B. return on assets. C. debt to capital ratio. Brian Jordan is...
Carey Company adheres to U.S. GAAP, whereas Jonathan Company adheres to IFRS. It is least likely that: A. Carey has reversed an inventory write-down. B. Jonathan has reversed an inventory write-down....
Which of the following items does the IMAs Management Accounting Competency Framework include as an important role, skill, or ability for successful managerial accountants? a. Data visualization b....
In the synthesis of the keto acid just given, the dicarboxylic acid decarboxylates in a specific way; it gives Explain. HO rather than HO
Suppose that X and Y are independent, continuous uniform random variables for 0 < x < 1 and 0 < y < 1. Use the joint probability density function to determine the probability that
The lifetimes of six major components in a copier are independent exponential random variables with means of 8000, 10,000, 10,000, 20,000, 20,000, and 25,000 hours, respectively. (a) What is the...
Contamination problems in semiconductor manufacturing can result in a functional defect, a minor defect, or no defect in the final product. Suppose that 20, 50, and 30% of the contamination problems...
By carrying out the audit of the financial statements in the Property, Plant and Equipment area, we were able to determine the reasonableness of the balance of the vehicle depreciation account. The...
The link between service delivery and external communications has a profound impact on customer perceptions of service quality. If you were to execute a service blueprint for dairy queen store and...
The city of marlohaven has a december 31 fiscal year end, during 20x5 marlohaven levied $1000000 in property taxes. the following details are expected collection of marlohaven's general fund property...

Show that if n is a positive integer, then k +4 n(3n 7) k= 1 k (k

Question:

k +4 n(3n 7) k= 1 k (k + 1 )(k + 2) _ 2(n + 1 )(n + 2)

Step by Step Answer:

We use induction If n 1 then the lefthand side has just one term na...View the full answer

Discrete Mathematics and Its Applications

Students also viewed these Statistics questions