k + 6 k+6 Hint: 126 = -te 3 Assume that n is a positive integer. Compute k+1 k3 + 3k² + 2k* k=1

Q: ve or disprove formally and precisely that the product of two consecutive integers is ays even (for…

A: Product of two consecutive integers

Q: By using the binomial theorem, evaluate : (102)* , (97)5, (1.01)3 2)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Subtract (5t+ 20t - 11) from (t- 9) O -4t2 – 20t +2 O - 6t2 + 20t 20 O 42 + 20t + 2 O -4t3 + 20t + 2…

A:

Q: (1) What is gcd(31212021 + 3, 31212021 - 3)? I am aware of 3121 is a prime number, and 2021 is…

A: # we are entitled to solve one question at a time, please resubmit the other question if you wish to…

Q: If n is a positive integer with (n + 1)(n + 3) is odd, then (n + 2)(n+ 4) must be a multiple of 1) 6…

A: Given:  (n+1)(n+3) is odd We will get an odd number from product of two numbers only if the two…

Q: (x – 2y2)5 ·+ bx³y* + •…· | ||

A: It is an important part of statistics . It is widely used .

Q: Which binomials are correct for the roots 7 and -2? F oudy O (x-7)(x-2) O (x + 7)(x-2) O (x+7)(x+2)…

A: The given roots are 7 and -2.

Q: (n-1)! Use Euler's theorem to prove that if n is an odd integer, then n divides 2 -1.

A: Using Euler theorem to prove it.

Q: Give an example of (a) a composite number of the form 2º – 1, where p is an odd prime. (b) a…

A: b) Here we need to find an example of a composite number of the form  22n+1 where n is a non…

Q: Questions: Confirm that gcd(30,40) * lcm(30,40) = 30 * 40. Find integers a and b such that 30a…

A: The gcd(30,40) is 10 The lcm(30,40) is 120.

Q: not use ai please

A: Explanation:1. Then, 3n + 4 = 3(2k + 1) + 4 = 6k + 7 = 2(3k + 3) + 1 (3)2. By definition of odd,…

Q: Show that 2 x ²dx (x²+1)²(x²2x+2) S 81 Z 775 50

A: FORMULAS:1.If f(x)=p(x)q(x) and degree of q(x) is greater than p(x) by atleast 2 and q(x) have only…

Q: Consider the statement, "For all integers a and b, if the product of a and b is even, then a is even…

A:

Q: Q-4: i. ii. iii. iv. V. Consider the integers a = 675 and b = 891. Find: The prime factorization of…

A:

Q: Discrete Math

A: According to the given information, Suppose that:

Q: How is duality connected to the principle of reciprocity in number theory?

A: To find: How is duality connected to the principle of reciprocity in number theory.Duality and the…

Q: (b) If a, b and c are integers such that b| a and b| c, then b | (2a – 3c).

A: We have to proof

Q: Determine which binomial is a factor of 3+ 22 40a +64 O (2 8) O (x- 2) O (a + 2) O (a + 4)

A:

Q: this

A: We use definition of t(n).

Q: p Pq C N-n N-1

A:

Q: Prove or disprove: There exists an integer a such that 14 | (3a – 5) and 21 | (2a +3).

A:

Q: (1) The family spend 15% of their New Zealand dollars on a tour. Calculate the number of dollars…

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Q: Induction: m (2n-1); nz n=? • Prove by Mathematical 1+5+9+...+(4n-3)

A:

Q: screte Math Prove by contrapositive For all integers m and n, if m + n is even, then either m…

A: To prove that for all integers m and n, if m + n is even, then either m and n are both even, or m…

Q: A local city wants to compare the number of those with a car and those without a car, represented by…

A: Given,          A local city wants to compare the number of those with a car and those without a…

Q: Find 2(2k + 2). k-3 O 8+ 10+ 12 + 14 + 16+ 18; 78 8+ 10+ 12+ 14 + 16; 18 O 10+ 12 + 14 + 16+ 18; 8 O…

A: ∑k=38(2k+2)=(2×3+2)+(2×4+2)+(2×5+2)+(2×6+2)+(2×7+2)+(2×8+2)…

Q: Discrete Math Let k be a positive integer. Use induction to prove that (k −1)^(n+1) +k^(2n−1) is…

A:

Q: Show that if n is an integer and 5n + 6 is odd, then n is odd. (Use contradiction.)

A:

Q: Simplify (56 +47)(-6 - 7)

A: