Use the permutation and combination formulas to prove the following. +k – 1) (n + k – 1 (b). V k, n e Z*, п—1

Q: Equating the coefficients of corresponding powers of t gives 2/3(13A2 + 2) = 10A2 + 1, (2.200)…

A: 2313A2+2=10A2+1   .....(1)2935A3+10A2=10A3+2A2     ...(2) We need to solve the equations to find the…

Q: Q2) Let X, Y be i.i.d with binomial PMF. Find PMF ofU= X+Y and W = X-Y.

A: Dear student, If you find this solution helpful please upvote ? it.

Q: Q1: Prové by induction nzZ! ☆ (1- 1 htI ( Here JJ (Pi") stande for froduct) means (I- I

A: A detailed solution is given below.

Q: Evaluate fff. 5y²dV where E is the reqion below x + 3y + 6z = 9 in E the first octant.

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Q: x2+1 =0 Has soluion in R

A: Solution:

Q: Consider a, = V4n² + 3n – 2n for n > 1. %3D -

A: Introduction: The sequence is a set of functions with the set of natural numbers as the domain of…

Q: If сх 3D су (тod n) and c >0 then а) х 3Dу (тоd сп) Ь) х%3D у (тod n) с) хну (тod") а) None of thes-

A: We have to solve given problem:

Q: Z1 is complementary to ZM 22 is complementary to ZM Z1 = 2 Given: Prove: M R 2

A: Given: ∠1 is complimentary to ∠M. ∠2 is complimentary to ∠M. To prove: ∠1≅∠2 According to the…

Q: Use substitutions to waite (In t)at, for seyo (1n ms of と in 0,9 € N, aE IR E IN, a E IR, a#0 where

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Q: 0 <m < n such that am = e. (Hin

A: Subgroup generated by any element in a finite group will have at most n element where n is order of…

Q: If f(z, y) – e . In(9y) , then fz is given by: O - 9e In(9y) o - 27 e In(9y) O 9 e In(9y) O 27 e…

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Q: Solve the following forr W=4xc for c %3D C = (Type an exact

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Q: Which of the following is NOT true about the DE: 6xr?ydx+2x³dy=0?

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Q: Answer the following question accordingly: a) Let A=|2 3 -1 3 a and B-l= where %3D 2 5 a ato and a $…

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Q: 1. Given s=6x720: Find a) whure y is at eauilibriuma is increosing <) whe y is docieosing 5) where

A: Given y'=6x2+7x-20 So, equilibrium of y will exist where y'=0…

Q: Determine the general solution of the following Efuler equatión for x>°, g-2xy-4y= \0x using the…

A:

Q: (a) Find the least positive k E N such that 3* =10 1. (b) Using this k, prove: for all m e N, 3m =10…

A: (a) find the least positive k∈ℕ such that 3k≡10 1 b) using this k prove that : for all m∈ℕ 3m≡103m÷k…

Q: Evaluate the following. SP S: z = 13 - 4x + 6y, 0 Sx S 5, 0sys5

A: We have to evaluate the given double integral.

Q: d x" = nx"-1 de 4. Prove that NɛQ

A: ddxxn=nxn-1 ;   n∈Q

Q: Q3: Prove that (9":n e Z} S {3":n Ee Z} but {9":n e Z} (3":n E Z}.

A: To prove:  {9n:n∈ℤ} ⊆{3n:n∈ℤ} but {9n:n∈ℤ} ≠{3n:n∈ℤ}

Q: The number of the element(s) of order 2 in Z2 O D6

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Q: 2. Find p and q such that |5x - 2| ≤4 implies Ps 23x-4 5 ≤q.

A: Given |5x-2|≤4

Q: A second solution y2 for the DE z'y" - 4ry +6y = 0, can be obtained by reduction of order with the…

A: According to quetion given Differential equation x2y"-4xy'+6y=0

Q: 8a, 2+ 225n for n> 2 with initial conditions ao 7, a1 83 %3D

A: Given: an=-6an-1-8an-2+225n for n≥2 with initial condition a0=7, a1=83. To find: The solution of the…

Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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Q: For positive integers n and k (k sn+ 1), the kth term of (a + b)n is given by

A: The binomial expansion of (a+b)^n is

Q: D If/2ty -P and 25=n(ytoc) n-T s in terms of n and P express only MS

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

Q: 1 Q4) If vZA =, such that AA" = I. Find x?

A: Transpose of matrix

Q: The first three terms in the expansion of (1 + ay)^n are 1, 12y, and 68y^2. Find a and n.

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Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: Prove the following: 1) 1+3+5...+ (2n-1) = n²

A: *By Bartleby policy I have to solve only first one as these are all unrelated  problems.These are…

Q: Suppose x-j, for j-0, 1, 2, 3 and it is known that Find Po123(1.5). P₁1(x)=x+1, P₁2(x)=3x-1, and…

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Q: Prove for r ≠ 1 that ∑_(k=0)^(n-1)(rk)=(1-rn)/(1-r). If ∑_(k=0)^(n-1)(rk), then compute s(1−r) =…

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Q: Prove indirectly: "V n E Z, 4 ł (n² – 2)."|

A: Ans:Let us assume that 4/n2-2;∀n∈zthen we have there exist a positive integer k such…

Q: Z1 is complementary to 2; 2 is complementary Given: 2 B 3 A E to 23 Prove: BD || AE

A: Prove that BD∥AE.

Q: Q2// A :- Compute for the following at t=1 z = re²", x = t², y =t-1

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

Q: Verify that the Diophantine equation x² + y² where d'(n) and d"(n) are the numbers of positive…

A: We will first show that product of two square numbers can be expressed as a sum of two square…

Q: Use Gauss's trick to determine H(n)=1+5+9+13+...(4n-7)+(4n-3)+(4n+1) I got n(4n+2)/2 is this…

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Q: HW KLX) = 2x+5 7 -1. Find ke-²¹ (x) 2. Prove by kok orklok

A: Let's find inverse function.

Q: In the expansion of (2r + 1)", the coefficient of the term in x is 40n, where n e positive integers.…

A:

Q: The fourth term in the expansion (2r + y)' is

A: The equation for the combinations n taken r at a time is equal to Crn=n!n-r!r!.  The continued…

Q: 4. If LM = 41 - 2r and NP = 7x + 5, find LM. %3D

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Q: For f(æ) = 4 In(æ) + 2² – 3.4x + 10 with æo = 1.5 and æ1 = 9.3 apply steps of the method of 10 false…

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Q: Z1 and 22 are complementary Z3 and Z1 are complementary ВС | DE Given: Prove: A 1 3 D E

A: Given: ∠1 and ∠2 are complementary.∠3 and ∠1 are complementary.

Q: use the convolution theorem to find L'{2+1 -1 4 Specifically s²(s²+1)

A: Given,        L-14s2s2+1=

Q: Let c, = M and Cn = 2cn-1 - 1 for Vn eZ+ - {1}, find the explicit formula for the nth term for n…

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Q: Solve the recursion by substitution for  T(n)=2T(n/4)+n2 where T(1) =1

A: To solve by putting T(1)=1

Q: Given the set of multiples of 5 defined by 5Z:= {m: m = 5n for all n e Z} together with the…

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Q: 3 (a) Given that T= 2n12g , express I in terms of T, g and n. %3D

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Q: In Euler's method, wr = y(tx) for k=1, · .., n. Select one: O True O False

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…