3. Prove the following identities for Binomial Coefficients (by using the factorials) A. (1) = n B. (1) = n n(n-1) = 2 C. (2) D. (R) = (k)

Q: Find the first three terms of the expansion (4 – 2x)³.

A:

Q: Prove that if n is a +ive integer,

A: Given that, M xddxnf(x);p = (-1)npnF(p) We can prove this by mathematical induction.

Q: (a) Find the binomial expansion of (1 – x)-1 up to and including the term in x?.

A:

Q: 20. What is the sum of all the exponents of the expansion of (8x-7y)¹2 a. 163 b. 150 c. 953 d. 156

A: Introduction: The binomial expansion theorem is very useful in expanding a binomial terms with…

Q: (QuestionID:T1Q2.4) What is the coefficient of 2° in the binomial expansion of (2² – 1)5 ? Choose…

A: What is the coefficient of x3 in the binomial expansion of (x2-1)5

Q: Given that m*n=3m-n, find the value for y for which (2*1)*y=0

A: Given mn=3m-n

Q: Use the Binomial Theorem to show that 50 E)(-2)" = 1. %3D

A: Binomial Theorem:

Q: Find the specified nth term in the expansion of the binomial. (x − 7y)5,    n = 3

A:

Q: Write the binomial expansion for (x+3)°. ..... (x + 3)° =D

A: Solution...

Q: Find n(A)   A= {1/2, -1/2, 1/3,- 1/3,......1/10, -1/10}

A: Compute n(A) as follows.Assume a set B with 20 elements.B = {1,−1, 2, −2, 3, −3,......10, −10}.

Q: 3. Determine the 4th term of (3x+ 2y3 6 using The Binomial Theorem.

A: We will find the 4th term

Q: (4 – 2æ)".

A:

Q: Prove the following using the binomial theorem: ()=()+ 2n

A: In this context, the aim is to prove 2n2=2n2+n2.

Q: Calculate the binomial coefficient. (13'

A: To calculate the binomial coefficient

Q: Use the binomial theorem to expand the expression (u - 5v)¹

A:

Q: 2021 2. Expand (1 + v3i)“ recall the binomial theorem.

A:

Q: Find the specified n-th term in the expansion of the binomial. (x+y)10, n = 3 O 44 xy² O 47 xy2 O 46…

A: Let' s write the Nth term for the binomial expression , ( a + b ) N  Here a and b are real numbers…

Q: nv n=1

A:

Q: Find the first three terms of the expansion (4 – 2x). 4°(1- 폴 + 쫄 +…) O b. 2°(1 + 꼭 + 플 + …) Oc…

A:

Q: п n 9. Using the Binomial Theorem, show that Σ = n 2"-1. k k=0

A: We need to show that- ∑k=0nknk = n2n-1

Q: (c) How many strings of four decimal digits have exactly three digits that are 9? (d) Write down the…

A: We have to find the coefficient.