Given N is a positive integer less than 31, how many values can n take if (n + 1) is a factor of n!? 18 16 12 20

Q: d) How many 4 digit numbers can you make from the elements of A without repetition contain the…

A: We shall solve first question only as per answering guidelines. If you want others to be solved…

Q: 7 8. The sum of two consecutive even integers is of their product. Find these integers. 24

A: Topic- basic maths

Q: What is the solution to 8(2**³) = 48? In 6 1 x = -3 In 2 x = 0 In 48 -3 In 16 3 4 x = In4-3

A: Use one exponent property of logarithms log xy=y log x. To solve a linear equation in a variable x…

Q: 21. Given that "( = "('3, the value of the integer n is 6 D 3

A: To find the value of n in the given problem, we use the definition of binomial coefficients.

Q: If d|a + b, then d|a or d\b. Every integer n can written as n = 2km, with k > 0 and m is odd.…

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Q: 10. If n is a negative integer, then 1- n² is an integer for how many values of n? (A) None (B) One…

A: Simple calculation problem...

Q: 19. What is the value of (pk) when p is prime and k is a positive integer?

A: We know that the value of the Euler ϕ-function at the positive integer n is defined to be the number…

Q: 6) Given a 4-digit number to form two 2-digit numbers with its first two digits and its last two…

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Q: How many three-digit numbers can be formed under each condition? (a) None of the digits can be 9.…

A: Here 3-digits numbers can be formed. a) 9 not be used b) lead dgits 0 to 4

Q: If n is a natural number, the number 3dn+4 – 4³n+3 is divisible by: A) 14 в 15 C 16 D 17

A: Given :n is natural number, the number 34n÷4-43n÷3

Q: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: If both x and ( ++ ) are positive integers, what is the least possible value of x? 10 120 O 90 O 60…

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Q: The small positive integer n for which (1+i)=(1-1)" is =. ........ 8 4 12

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Q: If n is an integer and n 2 1, then the expression 4" + 4-1.3+42.3+ 4-.3+4".3++4 3+ 3 is equal to

A: (c) is correct We have to find the value of 4n+4n-1·3+4n-2·3+4n-3·3+4n-4·3+⋯+4·3+3

Q: For which natural numbers n is n3-10n2+28n-19 a prime number

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Q: 2n+1 In Section 8, Example 2, if you follow the same procedure for the result is Зп-5 N = + ??? 9e 3…

A: Introduction: The theory of functions' limits is the foundation of calculus because these are the…

Q: (c) If n is an integer greater than 2, then for all integers m, n does not divide m or n + m # n m.

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Q: 3. Are the following statements true or false? Justify your conclusions. (a) For each integer a, if…

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Q: Show that (a) 8n −3n is divisible by 5 for all natural numbers n.  (b) n2 −n +41 is odd for all…

A: expansion of (a+b)n = hco an bo + nc1 an-1 b1 +.......... +ncn ao b n

Q: 10. The square of any integers is of the form 5k, 5k + 1 or 5k + 4.

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Q: 1 A1 5 a b C d for some integers а, b, с, d. What are the values of these integers (in order a, b,…

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Q: N is less than 60. All the factors of N are bigger than 60. How many natural numbers can be N?

A: It is given that N is less than 60. N<60

Q: For the natural numbers that are multiples of 3 and less than 76. a. What is the largest of these?…

A: The natural number that are multiple of 3 and less than 76 are  3,6,9,12,........,72,75

Q: 1. For all positive integer n, which of the following expression is divisible by 6? A) 7" – 1 C) 5"…

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Q: 5. Find the sum of all the odd integers from 100 to 200, inclusive. a. 7,000 b. 7,500 6. How many…

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Q: If (n+3)! An? + Bn + C (n+1)! determine the integer values of A, B, and C.

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Q: 1-n 15 dr = V고 +1 -1

A: Please go through the attached solution.Thankyou . Best regards.

Q: If a, b, and c are even integers and 3a2+9b3=c, which of these is the largest number which must be a…

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Q: The small positive integer n for which (1+i)?n=(1-i)ên is 4 12 2 8

A: Given:- (1+i)2n =(1-i)2n To find:- Smallest value of n for which give expression true

Q: 2(5) – 3(1 – 6) Is even integer?

A: If an integer is divisible by 2, then it is called an even integer. For example, 2,4,6 etc. are even…

Q: How many integers from 1 through 82 must you pick in order to be sure of getting at least two of…

A: The possible remainders when a number is divided by 5 are 0, 1, 2, 3, and 4. Now by pigeon hole…

Q: 5. Find all possible single digits that can be placed in the square so that the number 1,427,4 2 is…

A: Given number :- 1,427,4_2  Find:- All possible single digits that can be place so number divisible…

Q: The number of divisors of a natural number n is 15 then the number of solutions (n,m) of n-m? = 4(m…

A: Here, the given equation is n-m2=4. Here, n∈N and m∈I. Given that, n must have 15 factors. If m=0,…

Q: The value of (n + 1)! is O (n +1) - n! O n- (n+ 1)! O n- (n – 1)! O (n +1) · (n+ 1)! O none of the…

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Q: A boy imagined four-digit multiple of 5 with different digits. If the first digit is erased, the…

A: Given that  A boy imagined four digit number If the first digit is erased the obtained number is a…

Q: Please help me!

A: For the first part of the Q: We need to write one digit on both sides of 57 to make the number…

Q: 60. For what positive integer k is k+5 a factor of k2+11 while k+11 is a factor k2+5? ANS. 7

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Q: 6. If x is any positive integer, which one of the following terms could be added to the sum of 2x +…

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Q: 5. (a) Find a formula for the number of square tiles in the figures below. n= 1 n= 2 n= 3 n= 4

A: To find a formula to determine the number of square tiles in the given figures.

Q: 134. Ify = -3(x + 2)² + 1, where x is an integer, what is the greatest possible value of y? А. - В.…

A: Let's find.

Q: If (n+1)! An? + Bn + С (п-1)! determine the integer values of A, B, and C.

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Q: 58. The integer k is the product of four different prime numbers. If k divided by 22 is a multiple…

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Q: 3 times an integer squared plus 6 times that same integer is equal to 105. Find one possible…

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Q: 3n<n! If n is an integer greater than 6.

A: As per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: 6. If the set R consists of the integers 1 to 10, inclusive, what is the greatest factor of the sum…

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Q: 2. For all positive integer n, the expression n -n+ 3 is always divisible by A) 6 only B) 2 and 3…

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Q: (c) For each integer n, if n is odd, then 8 divides (n4 + 4n² + 11).

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Q: if n zo is an integer, then n!=n(n-)3.21 ...

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.