5 find the quotient i15-as a" by long division meth od 1-a

Q: Show that (2i – 1) (2n)! for every positive integer n!2" n. i=l

A: We have to solve given problem:

Q: (5n)! 40"-n! is natural number for every natural number n. Prove that

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Q: 2. Find the root using Regula-Falsi Method a) x* - x - 10 = 0 Ans. x = -1.697 and 1.855

A: Follow the procedure given below.

Q: Give a formula for the nth positive even integer: Here is a theorem: 1+ 2+3 + ... + n п(n+1) n = Use…

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Q: 1. Which operation below does not change the value of any nonze ro number on oob A. Adding by One B.…

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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: I was asked to prove that 5^(2n+1) + 4^(2n+1) is divisible by 9 for all n that are positive…

A: SOLUTION-

Q: Let p be a prime, a ∈ Z. Prove that ap − a is divisible by p.

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Q: The general combinatorial formula for the nth triangular number (1, 3, 6, 10, 15, 21, .) is On+1Cn…

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Q: Show for all integers n> 1 that 7 I (3ªn+l – 5²n-1 ).

A: a) Prove 734n+1-52n-1 for all integers n≥1 by mathematical induction as follows. Basis step: For…

Q: Determine the nth term formula for the number of square tiles in the nth figure. an az az ag

A: From figure the first figure contains 2 boxes The second figure contains 4 boxes The third figure…

Q: 3 If the characteristic roots of 2 7 are A1 and A, the characteristic root of 7 are - 2 3

A: Given matrix is 3725 with λ1 and λ2 its eigen values.

Q: Date 262 Find tue minimugn to the consfraint of n?¢4y?-2n+8y -7=0

A: 5.2 We need to find the min of x2+4y2-2x+8y. Subject to constrain x+2y-7=0 Let f(x, y)=x2+4y2-2x+8y…

Q: Determine the nth term formula for the number of square tiles in the nth figure. an %3D as a2 az

A: Number of tiles in a1 is 2, n=1 Number of tiles in a2 is 4, n=2 Number of tiles in a3 is 6, n=3…

Q: When x is divided by 7, the remainder is 5. What is the remainder when 5x is divided by 7? Moreover,…

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Q: 7. Find a number t such that In(4t +3) = 5 (Give EXACT value)

A: Given that ln(4t+3)=5 we need to find "t"

Q: 96, a0ose -bsine =0 a'simo +baose asimo-baose Then,

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Q: Show that n := e2™i/n is a primitive nth root of unity in C. Verify that (S3 - )? = -3 in C. Verify…

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Q: Use the formula to compute In(1.11) correct to five decimal places. In(1 – x) = - x" n = 1 In(1.11)…

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Q: Recall the Fibonacci numbers Fn are defined by Fo = 0 , F1 = 1 and Fn Fn-1 + Fn-2 for all n > 2 .…

A: Consider the provided question, Fibonacci numbers Fn are defined by F0=0, F1=1 and Fn= Fn-1+Fn-2 for…

Q: Hefined or of length e colculated using Olnlan) operations n=2 then the

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Q: 5. Invent a positive integer a that has at least 8 decimal digits and a ones digit of 7. Estimate…

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Q: 3. Find integers s and t so that 1 7s+ 11t. Show that they are not unique. %3D

A: Apply the division algorithm, we get 11 = 7*1 + 4 7 = 4*1 + 3 4 = 3*1 + 1 Hence, 1 = 4 - 3*1   = 4 -…

Q: ) Prove that for all positive integers k, 22k – 1 is a multiple of 3.

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Q: 13. Solve the rccursive formula an = an-1 +1+2"-1 with ao = 0. Verify by %3D induction.

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Q: Infer a formula for Ak using factorization where A =

A: Calculate eigenvalues: 1-λ-62-6-λ=0-6+6λ-λ+λ2+12=0λ2+5λ+6=0λ=-2,-3

Q: 5 М — 11 Find formulas for the entries of M", wheren is a positive integer. M" =

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Q: Factor 10+ 4i into product of primes Z [i], (Hint: Ille= (2)(2)(29)) in %3D

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Q: 6. Find the root using Regula-Falsi Method a) x* -x- 10 = 0 Ans. x = -1.697 and 1.855

A: As per our company guidelines, we can solve first question for you. If you want other question to be…

Q: to binary. II. Show that any weight not exceeding 2 - 1 may be measured using weights of 1, 2,…

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Q: Find integers p and q so that 17p + 45q = 1. Show your working steps.

A: Here we have to find the integers p and q so that  17p+45q=1

Q: 5. Find the value of AB. B AL 5 in 5 in X16 in

A: We have to find AB

Q: the pth term of AP is a and the qth term is p,prove that it's nth term is (p+q-n)

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Q: 8. Show that no prime number of the form 4k +3 can divide a number of the form n2 + 1.

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Q: Find a polynomich of Jegree 4 with Zeros x = 1₁ x=2, and x=i.

A: Given polynomial has zeros x=1, x=2 and x=i. Therefore (x-1) ,(x-2) and (x-i) is factor of…

Q: (5n)! 40 n! is natural number for every natural number n. Prove that

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Q: 22. Without expanding the power, what is the yf term in the expanded form of (x- 2y)? Show your…

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Q: 5 Let flx) -5X+3Xh emd gx) = 3X+2X+) in 7[x].Determine the quotient ane remainder upon dividing #00…

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Q: 6. Describe the left cosets of SL2(R) in GL2(R). What is the index of SL2(R) in GL2(R)?

A: For a group G with a subgroup H, the left coset is defined by gH=gh:h∈H∀g∈G.  Since g can be…

Q: How many multiplicity of - 1 are there in the roots of x +3x2 + 3x+1 0? O 1 O 2 3 O 4

A: Given equation  x3+3x2+3x+1=0

Q: Number theory

A: Assume a=x2

Q: lim, o0 (3 In (4 + z) – In (2x³ – 5)]

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Q: Expand (2r- 3) using Pascal's Triangle.

A: Expand (2x - 3)3 using Pascal triangle. According pascal triangle we use n value and take row of…

Q: let us assume that /3 is a rational number .show that V3 = where a,b are co – primes b

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Q: Find (with proof) the residue of 320222022 when dividing it by 31.

A: Given number is 320222022 Let the remainder(residue) be x when 320222022 divide by 31 x=32022202231…

Q: 2n + 1 6n+3 Show, by using congruence, that 11 divides 3 +2 for n21

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Q: 3. Prove that if n is a triangular number, then so are 9n + 1, 25n + 3, and 49n+ 6. Hint: Recall…

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Q: 3. Prove that if n is a triangular number, then so are 9n +1, 25n + 3, and 49n + 6. Hint: Recall…

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