When n is even the product n n 1 n/2 is divisible by select one?

When n is even the product n n 1 n/2 is divisible by select one?

Hence, n(n+1)(n+2) is divisible by 24.

Where m is some integer for any positive integer n prove that N 3 N is divisible by 6?

Out of three (n – 1), n, (n + 1) one must be even, so a is divisible by 2. 2. (n – 1) , n, (n + 1) are consecutive integers thus as proved a must be divisible by 3. Thus, n³ – n is divisible by 6 for any positive integer n.

Is divisible by 2 for every positive integer n?

Expert-verified answer ∴ n = 2q or n = 2q + 1 where q∈Z. Thus, in any case, n² – n is divisible by 2. Thus, n² – n is divisible by 2 for every positive integer n.

Is positive integer n divisible by 4?

Hence, P(n):7n−3n is divisible by 4 is true.

Is the positive integer n even?

If n is a positive integer, then n is even iff 3n2+8 is even. n2 + n + 1 is a prime number whenever n is a positive integer.

Are 0 and 1 only the values of the remainder R when a positive integer A is divided by 3?

The values of the remainder r, when a positive integer a is divided by 3 are 0 and 1 only.

How do you prove that N 3 is divisible by 3?

We can say that (k + 1)3 – (k + 1) is divisible by 3 if k3 – k is divisible by 3. Therefore, we can say that if the given statement is true for n = k, then it is also true for n = k + 1. Hence, by the principle of mathematical induction, the given statement is true ∀ n ∈ N.

Is M divisible by 6 statements?

Explanatory answer We need to answer if m is divisible by 6. The answer has to be a definitive YES or a NO. The test of divisibility for 6 is that the number should be divisible by both 3 and 2. From statement (A) we know that m is divisible by 3.

Is N divisible by 2?

Therefore, n2 – n is divisible by 2 if n is even. Therefore, n2 – n is divisible by 2 if n is odd.

How do you check divisibility by 24?

Hence a number will be divisible by 24 if and only if it is divisible by both 8 and 3. Option a: 35718. Sum of digits = 3+5+7+1+8=24. Since 24 is divisible by 3.

Is 7 a positive integer?

1, 2, 3, 4, 5, 6, 7…… are positive integers and -1, -2, -3, -4, -5, -6, -7…… are negative integers. 0 is an integer which is neither positive nor negative. On an integer number line, all numbers to the right of 0 are positive integers and all numbers to the left of 0 are negative integers.

Which of the following is an even positive integer?

Out of the following the integer which is positive and even is 4. Thus, option A is correct.

What are the possible values of remainder when a positive integer a is divisible by 3?

The values of remainder r when a positive integer a is divided by 3 are 0 and 1 only.

When a positive integer A is divided by another positive integer b then the possible values of remainder can be 0 1 or 2 only what is the possible value of B?

Here, a= Dividend, b= Divisor, q= quotient and r = Remainder. According to Euclid’s division lemma a 3q+r, where 0≤r≤3 and r is an integer. Therefore, the values of r can be 0, 1 or 2.

How is n divisible by 3?

We can say that (k + 1)3 – (k + 1) is divisible by 3 if k3 – k is divisible by 3. Therefore, we can say that if the given statement is true for n = k, then it is also true for n = k + 1.

How do you show that a function is divisible by 3?

Example Prove by induction that n3 + 2n is divisible by 3 for every non-negative integer n. Solution Let P(n) be the mathematical statement n3 + 2n is divisible by 3. Base Case: When n = 0 we have 03 +0=0=3 × 0. So P(0) is correct.

Which of the following is divisible by 3?

A number is divisible by 3, if the sum of its all digits is a multiple of 3 or divisibility by 3. Sum of all the digits of 54 = 5 + 4 = 9, which is divisible by 3. Hence, 54 is divisible by 3. Sum of all the digits of 73 = 7 + 3 = 10, which is not divisible by 3.

What is the divisibility rule of 4?

If the last two digits of a number are divisible by 4, the number is divisible by 4. If the last two digits of a number are 0’s, the number is divisible by 4 because 4 divides 100. For example, 324 is divisible by 4 because 4 divides 24, and 1500 is divisible by 4 because the last two digits are 0’s.

How do you prove that N 2 is divisible by 2?

Therefore, n2 – n is divisible by 2 if n is even. If n is odd, then (n – 1) is even. This implies that n * (n – 1) is also even since multiplying even number and odd number gives even number. Therefore, n2 – n is divisible by 2 if n is odd.

How do you know a number is divisible by 3?

Divisibility by 3 or 9 First, take any number (for this example it will be 492) and add together each digit in the number (4 + 9 + 2 = 15). Then take that sum (15) and determine if it is divisible by 3. The original number is divisible by 3 (or 9) if and only if the sum of its digits is divisible by 3 (or 9).