Question: 3. PROOF BY INDUCTION (a) Prove that for for every natural number n, the last digit of 6 is either 4 or 6. (b)

3. PROOF BY INDUCTION (a) Prove that for for every natural number

3. PROOF BY INDUCTION (a) Prove that for for every natural number n, the last digit of 6" is either 4 or 6. (b) Prove that for any natural number n we have 12+2+3+...+n == (c) Prove that for any natural number n we have 1 1 + + 1 1.2 2.3 3.4 1 n n +...+ = n. (n+1) n+1 (d) Prove that for any natural number n we have 1 1 1 1 + + + + 3". n

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 Mathematics Questions!

URLIVE CONDENSED CONSOLIDATED BALANCE SHEETS - USD ($) $ in Thousands Cash and cash equivalents Marketable securities Accounts receivable Allowance for bad debts Deferred contract acquisition costs,...

what do British Columbia's provincial authorities need to prioritize to enhance and convert the city of Vancouver into a world-class logistics hub? (five hundred words answer required) Introduction -...

Place the following 5 steps into an appropriate order for a proof by mathematical induction of For every natural number n 1, 10 * 1 + 10 * 2 + ...... 10 * n = 5 n (n + 1) Verify that 10 * 1 + 10 * 2...

(a) Prove that the following statement is true for every natural number n, by using a sequence of equivalences: (3n+2)? > 12n + 13. 4] (b) (i) Use proof by contraposition to prove that the following...

Consider a language L that contains the following items: 1. An in?nite set E whose elememts are called the expressions of L. 2. A subset S of E whose elements are called the sentences of L. 3. A...

4. Using induction, prove that: (a) 72n1 is divisible by 48 for every natural number n. (5pts) (b) 72n48n1 is divisible by 2304 for every natural number n. (5pts)

Show that the only bijections f: Z Z satisfying the following condition: for all a, b Z : f (a+b) = f(a) + f(b) (*) are f(x) = x and f(x) = -x. (1) Show that the functions f(x) = x and f(x) = -x...

A matrix is known as a permutation matrix if its elements are 0 or 1 and each row and each column only has exactly one 1. For example, the matrix X below is a permutation matrix of size 10 x 10....

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...

Use Direct proof or contrapositive proof to solve and write in paper of each proofs. 1. If m, ne Z, then {xzZ:mn|x} C{xzZ:m|x} n {x=Z:n|x]. 2. If A, B and C are sets, then A U (Bn C) = (AUB) n (AUC)....

How do governmental funds report capital outlay in fund financial statements? How do government-wide financial statements report capital expenditures?

The curve for which y" = 6 has a slope of -3 at its point of inflection (2, 3). Find the value of arbitrary constant C1. . 12 . 6 .-6 D. -12

Candy took out a loan for $ 4 0 0 , 0 0 0 to buy her home. How much of this loan is included in Candy's income? Question 2 options: a ) $ 3 0 0 , 0 0 0 b ) $ 5 0 0 , 0 0 0 c ) $ 6 0 0 , 0 0 0 d ) 0 e...

e dipuke monerts of CC, CHI, and CH, are n the arder. , -CI,

On January 2, 2020, Pharoah Corp. issues a $8million, fiveyear note at LIBOR, with interest paid annually. To protect against the cash flow uncertainty related to interest payments that are based on...

Case: In a study, it was reported that undergraduate students had an average credit card balance of $ 2800. This figure is an all-time high and has increased 44% from the previous five years. Assume...

You can accept a lottery jackpot payout of $1 billion dollars or wait 35 days for the parables total payout. Which do you choose and why? Follow-up Answer the following questions: Would your answer...

1. Based on the information in Figure 2, illustrate in a diagram how Bruno would decide to use more robots in his firm to minimise production costs. Your diagram should have the number of workers on...

Create a 200 word summary on the Juvenile Justice System than and today. Describe The Juvenile system and provide a generalizable definition. Highlight the issues in the Juvenile system and why this...

As a result of a loan from Plains State Bank, Akers Company signed a 120-day note, dated March 12, for $15,000 that the bank discounted at 8 percent. Write the entries for the maker in general...

In arranging for a 90-day loan from a bank, Markey Company has the option of either (1) giving a $62,000, 10 percent interest-bearing note, dated November 3, that will be accepted at face value; or...

On April 3, B. M. Sibon gives a 60-day, 10 percent note, dated April 3, to Crosier Company, a creditor, in the amount of $6,430. a. What is the due date of the note? b. How much interest is to be...