Which of the following statements best justifies In(n+ 1)

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: To show the representation of an even integers is 2k and that for odd integer is 2k+1 or 2k-1 by…

Q: Given that the expression (n²+n+1) n! can be written as a(n + 2)! + b(n + 1)! + cn! where a, b, c…

A: The main objective is to find the sum value.

Q: Problem 4 [25 points]: Contradiction Given a proof by contradiction of the statement: If n? + 11 is…

A:

Q: Prove the following statement: 22 +23+24+... 2n+1 = 2n+2-4

A:

Q: find a Positive integern for which the equality holds %3D

A:

Q: Give a direct proof of the theorem “The sum of any two odd integers is even”.

A:

Q: n² + n+ 8 2 He has just shown you a convincing proof that if the equation is true for any integer k…

A:

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.

A: integer  which have 2 as one of their factors are called even numbers. The integer  which do not…

Q: Prove that for a positive integer n we have that 33n+3 – 26n – 27 is divisible by 169. - -

A: The given expression is: 33n+3-26n-27 This is to be proved that the expression is divisible by 169.

Q: So there are no real life exmaple of this? You must use math to prove that?

A: Here question is, there is no real life example of below ? Question- 1 cookie divded by 0.5 people,…

Q: 6) Let n be a positive integer such that 7 | (52n-1 +22n-1). Prove that 7 || (52n+1+22n+¹). (Hint:…

A: Since, given that  52n-1+ 22n-1  is divisible by 7 .  We have to prove that  52n+1+22n+1 is also…

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

A:

Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's Theorem: If p is a prime and a is a positive integer and not divisible by the prime p, then…

Q: (b) Show that 1 11 2 k(k + 2)(k + 4) 96 k=1

A: Given series is ∑k=1∞1kk+2k+4

Q: Use induction to prove that the product of any three consecutive positive integers is divisible by…

A:

Q: Give a direct proof of the following statement. If x is an even integer, then x² – 6x + 5 is odd. |

A: Remark: We know that addition or subtraction of an even and an odd integer is always an odd integer.…

Q: 9. 10. What is t divisors?

A:

Q: fermat's theorm states, if p is prime & a is a positive integer not divisible by p then-------- and…

A: Fermat's states that if p is a prime and a is a positive integer not divisible by p, than ap-1≡1 mod…

Q: Show that if k is a positive integer, then (15k+4)/(10k+3) is in lowest terms.

A: We use the concept of Ring theory that a fraction is in lowest form if the gcd of numerator and…

Q: 1.5 Inx - In(x2 - 1) + 2ln(x + 3)

A: Logarithm simplification

Q: Show that if n2 -3 is even, then n is odd. Prove by contrapositive For the toolbar, press ALT+F10…

A: We need to prove by contrapositive.  The contrapositive statement of "If p then q" is "If not q then…

Q: 11) | 8 + 4n| 4 -10 > 3 -8 -6 -4 0 2 12) 1 + −1 + 4m ≥ 32 -8 0 + + 4 8 12

A:

Q: Mathematically speaking, we can say that integer y is a root of a when it's possible to take some…

A:

Q: Suppose that b and c are integers where 9b = 12c. Then 9|c and 12|b.

A:

Q: Let n be an integer, use the definition of even to prove that 10n+ 4 is even. 10n+4=0x0 Since is a…

A: Let n be an integer. To prove that for any integer n the number 10n+4 is even. An even integer is…

Q: i do not undertstand where the 8 has come from in q2c

A: Part c,            4log32-log34-2log33-log312

Q: The following is a valid identity for the natural numbers, true or false? n(n +1)(n +2) P(n):13 +23…

A: The solution is given as

Q: The representation of an even integer is 2k; and that for odd is 2k+1 or 2k-1 for some integer k.…

A: Given the statements: The representation of an even integer is 2k for some integer k. The…

Q: Which of the following statements are correct? (Select all that apply.) (2“): = 2* z*(1+ 2') = 2" +…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.