If the coefficients of rth, (r + 1)th, and (r + 2)th terms in the binomial expansion of (1 + y)" are in A.P., then prove that m² - m (4r + 1) + 42² - 2 = 0.

Q: In the expansion of (2 + 4y?) a. How many terms are in the expansion after like terms have been…

A: We will find the answers of all parts using binomial expansion.

Q: Determine the coefficient of x3 in the binomial expansion of (1 + 5x)½ by completing the given…

A:

Q: 1) (a) Determine the simplest form of the expansion of (2x4 - 1) 4. 4x (b) Determine the coefficient…

A: Consider,(1) (a) Given,(2x4−4x1​)4use the binomial theorem formula to simplify the given…

Q: By taking the antiderivative of the binomial expansion, prove the following: + 1² ( 1 ) + 1² (2) 2…

A:

Q: Find the coefficient of a-2 in the binomial expansion of  (27a2 - (1/81a3))9

A: Let us consider the expansion x+yn The binomial expansion is obtained as x+yn=∑k=0nCknxn-kyn

Q: Expand with help of Binomial Theorem (- +)

A: Using the Binomial theorem, the binomial expansion formula for (a+b)n is given by the formula,…

Q: Expand the following using the Binomial Theorem or Pascal's Triangle: (x- 2)* a. x*-8x3 + 32x + 16…

A: Binomial expansion formula (a+b)n=C0nan+C1nan-1b+C2nan-2b2.......................Cnnbn

Q: 4. Find the expansion of (x + y)6 using Binomial Theorem.

A:

Q: a. Coefficient of x1/y21 in the expansion of (3x-2y)38 b. Coefficient of x23y41 in the expansion of…

A: The expression, nr can be defined by the formula, nr=n!(n-r)! r! .

Q: Write down the expansion of : 4 1 3x 2 by the binomial theorem.

A:

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

A: We will find the 4th term

Q: Write out the full expansion of (x + y)^7 using either binomial coefficients or Pascal’s Triangle to…

A:

Q: 1. Use the binomial theorem to fully expand (x² - 2y)4. Expectations Each term of the full expansion…

A:

Q: 24 + * ? 8 What is the coefficient for the yl8 term in the expansion of (5x°y²

A: We use the Binomial Theorem to answer the given question.

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

A:

Q: obtain the binomial expansion of (1-2x)^5 and use it to evaluate(0.98)^5 correct to 5d.p

A:

Q: 3 O Find the first three terms of the expansion of (1+x)(2x-1)

A: The given series is 3(x+1)(2x-1) We have to find first three terms of the given series. This can be…

Q: P1. In the binomial expansion of (2-3) written in terms of descending power of X, find; a the th…

A: Explained below

Q: Use the binomial theorem to prove that n <-D₁ (17) 3¹-*. 2″ = 2-D² k=0

A:

Q: (c) Find the term independent of x in the expansion of, 15 2 +

A:

Q: 2. (a) Given that (2 + x)" (1-x)" =+ pa³+qx²+7x+s, determine the values of P.4.9, and s. (b) Without…

A: Step 1: Step 2: Step 3: Step 4:

Q: a. Use the Binomial Theorem to write out the complete expansion of (x³ + y²)$ With all coefficients…

A: Binomial expansion

Q: Use the Binomial Theorem to find the coefficient of the r"y" term in the expansion of (2r – y)12

A: