Question: prove by induction 1^2+2^2 + 3^2 + ... + (2n)^2 = n(2n+1)(4n+1) / 3 for the first 2n positive integers.

prove by induction
1^2+2^2 + 3^2 + ... + (2n)^2 =
n(2n+1)(4n+1) / 3
for the first 2n positive integers.

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Q:

3. Let P(n) be the statement that 12 + 2- + ... + n- = n(n + 1)(2n + 1) /6 for the positive integer n. a) What is the statement P(1)? b) Show that P(1) is true, completing the basis step of a proof...

Q:

ONLY i and ii ONLY i and ii ONLY i and ii Question 2 This question has three parts and tests mathematical induction. (0) Give a recursive definition of the set P of all positive integers greater than...

Q:

can I get help with problem 18, (discrete structures) chapter 2, section 2 In Exercises 3-26, use mathematical induction to prove that the statements are true for every positive integer n. [Hint: In...

Q:

Some statements are false for the first few positive integers, but true for some positive integer m on. In these instances, you can prove Sn for n m by showing that S m is true and that S k implies...

Q:

Prove each of the following statements using mathematical induction. (b) For any n greaterthanorequalto 1, the factorial function, denoted by n!, is the product of all the positive integers through...

Q:

Please answer Question 2, 3, 4, 5, 6 and 7 Question 2 This question has three parts and tests mathematical induction. (a) Give a recursive definition of the set P of all positive integers greater...

Q:

Students at Monster University have found the parking information system helpful and enjoyed the recent free parking spot game. However, they often experience frustration when they enter a garage...

Q:

Show work/explanation where indicated. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the exam, or if you prefer, create a document...

Q:

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Q:

section 1; Paper size Letter 1. Fill in the blanks so that the resulting statement is true. A function f is continuous at a when three conditions are satisfied. . f is defined at so that is a real...

Q:

On December 31, 2012, Zugaboo Corp. issues 5%, 10-year convertible bonds payable with a maturity value of $5,000,000. The semiannual interest dates are June 30 and December 31. The market interest...

Q:

1 Explain how u found sales 2 Explain how u found percent of sale of op expenses (weight of each product) 3 Explain how much each product produces (most to least profitable) 4 Explain where money is...

Q:

Question content area top Part 1 Which of the following is the best strategy for controlling and managing your credit cards and open debt? Question content area bottom Part 1 A . Look for trouble...

Q:

The beta of a stock in your portfolio is .15. The covariance of the stock returns with the market returns is .003. The volatility (std deviation) of the market is closer to: A . 14% B. The standard...

Q:

Are use of symbols important in framing leadership as applied to the case study? Why/why not?

Q:

Why and how can corporate HRM never be context-free? What HRM theories do you know that argue in favour of the embeddedness of corporate HRM?

Q:

How and to what extent are the policies of Robert Bosch representative of the wider frameworks wherein they emerge?