Develop a simple expression for the entries of A", where n is a positive integer and 1 A = -IN -IN

Q: If x is any positive integer , then the sum of 6x and 11x is always divisible by what?

A: x is a positive integer. Find sum of 6x and 11x is divisible by what?

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Q: Find an expression for An, where n is an arbitrary positive integer.

A: Given: A=1423∈M2×2R

Q: (4) Prove in two different ways that if a is a positive r number, then (a + 1)" > a" + na"-1:

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

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Q: Find a positive integer n for which the equality holds = 1 2

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Q: Prove: For any positive integer n, x™1 - yl = (x- y) xy' (You may use the laws | of exponent in your…

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Q: If n is positive integer, Find (v3 + i)" + (V3 – i)".

A: To find the value of: 3+in+3-in Note that z=x+iy can be written as: z=r eiθ, r=x2+y2, θ=tan-1yx And,…

Q: A grain of rice weighs 0.03 grams. Assume 1 grain of rice is placed on the first square, 2 grains…

A: given that

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A: first we take a odd integer then we write in 2y+1 form then we transfer to difference of two…

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Q: a onvert the repeating decimal to - form, where a, b are integers and b 0. 54

A: Topic:- number system

Q: Every positive integer is the sum of at most two squares and a cube of nonnegative integers. O True…

A: consider 0  0=02+02+03 now  1 can be written as  1=02+02+13 now consider 2 2=12+02+13 now consider 3…

Q: (b) Show that įn is real, even though i or 9i is not.

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Q: Find the value of ,where n is a positive integer

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Q: (i) Deduce that the difference in the number of integers in the numerator and denominator of (* 2N N…

A: Properties of floor functions will be used.

Q: Find formulas for the entries of M", where n is a positive integer. M"

A: First find the Eigen Value and Eigen vector

Q: FIND THE SMALLEST n So THAT I

A: In this question, we have to find n for given |Rn|&lt;0.0001.

Q: Let i be a positive integer and A, = [-i+1,1]. Then U2, A

A: We have to use properties of union in this question.

Q: A(n) __________is a letter used in algebra to represent anynumber from a given set of numbers

A: In algebra, there are different set of numbers such as Real numbers, Complex numbers, Rational…

Q: Develop a simple expression for the entries of An, wheren is a positive integer and

A: The given matrix is A=112012. Observe that pattern as follows.

Q: Express 0.96 in the a/b where a and b are integers such that b=0

A: Given data:- The given equation is 0.96,

Q: asSin3x-Sn Sx =D

A: here question is sin3x - sin5x =0 so solve for x here we use sum to product identity sin3x - sin5x =…

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A: Given, 1n-1n+1    We have to prove the difference of the reciprocals of two successive integers…

Q: For each positive integer n, show that и(п)и(n + 1)u(п + 2)u(n + 3) — 0

A: To prove : μ(n) μ(n+1) μ(n+2) μ(n+3) = 0  for each positive integer n.

Q: Find the largest valuc of integer value ofk such that 1 (24 - 1) < 900. 5+7++

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Q: (c) Prove that n? + 1 is not divisible by 3 for every integer п.

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Q: Let M=( 3 Find formulas for the entries of M", where n is a positive integer. Mn = =

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Q: Find all positive integers n for which n1º +1 is divisible by 10.

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Q: Use the PMI to prove that 6" – 1 is divisible by 5 for every integer n > 0.

A: To prove that 6^n-1 is divisible by 5 for every integer greater that or equals to 0.

Q: Let i be a positive integer and A, = [-i+1,1[. Then N14= %3D

A: We have to find the first intersection first.

Q: Let n be a positive integer and M %3D Then M"

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Q: Show that 5 – V7 is an algebraic number.

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Q: Identify the real fourth root(s) of 256. O -4 O -2 O -1 O 2 O 4 O 2 and –2 O 3 and -3 O 4 and -4 no…

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Q: on 10 of 16 25628 49977 376? Find the missing number? O A) 40 O B) 38 OC) 39 O D) 35

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Q: Use the {\bf Cayley Hamilton Theorem} to come up with an expression for A" in terms of n when 1 A =

A: As you have asked more than one question, we shall answer first Que only. For others kindly post…

Q: Q prove that it ņ is an integer and 3A+2is odd then nis add

A: Given : n is an integer (3n+2) is an odd integer To prove : n is an odd integer

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Q: Find mZD. 6. D Write your answer as an integer or as a decima mZD = %3D

A: We have a right-angled triangle right angled at F we have to find angle D

Q: The product of all the natural numbers from 1 to n is written as n! it is read as "n factorial" true…

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Q: Find the positive integers n such that , the sum of positive divisor oln) = 24,

A: Sum of Divisors: Let the prime factorization of n be n=p1a1×p2a2×...×pkak Then the sum of divisors…

Q: a) Find the number of positive integers not exceeding 120 that are divisible by 3 or 4. 1 0 01 0 0 0…

A: As per our guides lines I answered only 1st part

Q: 5. Find all integers 100 ≤ n ≤ 999 such that the last three digits of n² is same as n.

A: To find: All integers  100≤n≤999 such that the last three digits of n2 is same as n.