3. If the coefficients of 4 consecutive terms in the expansion of (1+ x)" are k1, k2, k3 and k4 respectively, then show that k1 k3 2k2 |3D ki + k2 ka+kA k2 + k3

Q: What are the first and last terms in the expansion of (5x + 4y)*?

A:

Q: Expand 3x + 2y)7 using the binomial theorem. Simplify your final result.

A:

Q: (1+ 2x + 4x + 8x° + · · · )(3x + 3x* + 3x° + · · · )(x° + 2x° + 3x° + •..)

A:

Q: 6) Use Binomial expression in the form (a + b)¹: (x-2)5 + 10(x - 2)4 + 40(x - 2)³ + 80(x - 2)² +…

A:

Q: The coefficient of x²y4z5 in the expansion of (3x+y+z)¹¹ is

A: The given expression is: (3x + y + z)11 To find: The coefficient of x2y4z5 in the expansion of (3x +…

Q: Find the coefficient of x3y2z3w in the expansion of(2x + 3y − 4z + w)9.

A: The given expansion is 2x+3y-4z+w9. We have to find the coefficient of x3y2z3w.

Q: for

A:

Q: In the expansion of (x + y)16 which term has the same coefficient as x14y2? O a. x12,4 Oc x3y14 O d.…

A:

Q: Suppose a, b are relatively prime integers. (a) Show that gcd(8a, 8b) = 8. (b) Show that d = gcd(a +…

A: We will use the fact that if a,b are relatively prime integers, then : gcd(a, b) = 1

Q: Use Pascal's Triangle to expand the binomial (x + 1)° O 25 + 5x4 + 10x + 10x2 + 5x + 1 O g5 - 5x1-…

A: Pascal's triangle…

Q: Compute the coefficent of x8    in the expansion of (3x -2)13

A: The given expression is,

Q: 1. Suppose when using the Binomial Theorem an expansion turned out to be the expression as shown…

A: Formula for Binomial theorem: a+bn=an+nan-1b+nn-12!an-2b2+nn-1n-23!an-3b3+.....+bn Given expression:…

Q: 10 Which term of the expansion of (x²+4) ¹º contains x 20 Term number contains x 20

A:

Q: 5) Prove that the sum of two fourth powers of integers can never be three more than a multiple of 4.…

A:

Q: ow many subsets of the set {1,2,3,4,5,6} have at least 3 element

A: *Note: As per Bartleby's policy only first question is answered. Question 1. The set is given as…

Q: 5. • Use induction to show that for n ≥ 1 we have (3n+ 1) + (3n+4) + (3n+7)++ (6n-2) M n(9n-1) 2

A:

Q: which pair of binomials disproves Eric's ㅇ (z-2)(z + 3) ㅇ (z-2) (z + 2) z+3)(3 2)

A: Solution: