9. (a) Using Pascal's triangle, expand and simplify (1 + 2)- (1-2.r)". (b) Using the binomial theorem, calculate the coefficient of the r term in the HONOR 9X TRIPLE CAMERAion of (1+ r)".

Q: Expand (7 – 3x)“ in ascending powers of x, up to and including the 4" term. Hence, approximate…

A: We know (n+1)! = (n+1) n! Crn = n!(n-r)! r!

Q: 17. Expand using Pascal's Triangle or the Binomial Theorem. Be sure to show the setup. Then,…

A:

Q: A band of 19 pirates has stolen a sack of coins. When they tried to divide the fortune into equal…

A:

Q: Use binomial theorem to expand the binomial and express the result in simplflied form  (x+2)5

A:

Q: Use binomial theorem to expand (2+X)5 in ascending powers of x up to the terms containing x3  and…

A:

Q: State binomial Theorem.

A: Statement of Binomial theorem.

Q: Use Pascal’s triangle to expand the binomial. (d–5y)^6 show work:)

A: follow the procedure given below.

Q: Find the term indicated in the expansion .

A:

Q: Give a combinatorial interpretation of the coefficientof x4 in the expansion (1 + x + x2 + x3 +⋯)3.…

A:

Q: Expand in binomial theorem (2x-y)7

A:

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

A:

Q: Without expanding completely, find the indicated term(s) in the expansion of the expression.

A: We have given expression 3x2-y310 Then, fourth term of the expression…

Q: State and prove Binomial theorem and also find 18th term in the expansion of (2x - 3y)".

A:

Q: Find the coefficient of x8y6 in the expansion of (2x2-5y3)6 by using the Binomial theorem.

A:

Q: 2) Express 100C50 as a sum of two terms from Pascal's triangle.

A: Let us find thatThe  100C50 as a sum of two terms from Pascal's triangle.we know that the formula of…

Q: The 11th termof an A.P. exceeds than 10h term by 7 find the commondifference.

A:

Q: 4. Use the binomial theorem to find the first th ree terms in ascending powers of x of (1

A:

Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

A:

Q: 1. Find the 4th term of y (*- 2y*) using the Binomial Theorem.

A: The solution are next step

Q: 7th term of binomial theorem by (2x^2 + 3y^3)^8.

A:

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: Find the interval of convergence of x3n+2 Σ In(n) n=2 (Use symbolic notation and fractions where…

A:

Q: Consider the expansion of x 10 3

A: The binomial expansion of can be expanded as follows.   The formula for is defined as follows.

Q: 16. Find the term containing x18 in the binomial expansion of (x2- y)15.

A: A binomial expression is an expression of the form a+bn. This binomial expression can be expanded…

Q: (x³ + })*

A:

Q: State and prove binomial theorem with rational and irrational indices

A: Binomial Theorem: Bi means Two, Mial means Terms, i.e. the theorem applicable on two terms. Binomial…

Q: How many five-digit numbers are there where an even number of the digits in the number are even?

A: The number of five digit numbers where aneven number of digits in the number are even=??For these…

Q: 5. (a) Use Newton's binomial theorem to calculate √50 with 4 terms.

A:

Q: In two or more complete sentences, explain how to find the third term of the expansion of (2x+y)4.

A:

Q: 2. Use the Binomial Theorem to find the coefficient of x2000 in the expansion of (3x – 7)2021. 3.…

A: Recall: Binomial theorem :         a+bn = C0nanb0 +C1nan-1b1+...+Cnna0bn. Note :According to…

Q: . Explain how to use Pascal's Triangle to expand the binomial (3x-4y)".

A:

Q: How can the sum of k * (n choose k) = n(2 to the power of n-1) be proven akgebraically ?

A: Step 1: We have to prove that, Now by the binomial theorem, Now, differentiating the both sides of…

Q: Which term of the expansion of (x + 7)° contains x° Term number contains x°.

A:

Q: Explain how to use Pascal's Triangle to expand the binomial (3x-4y)^11

A: Given data: The given expression is (3x-4y)11. Here, the power of the binomial expression is 11.…

Q: Find the coefficient of the term involving x* in the expansion of 3x – - -262444 c. -252440 а. b.…

A:

Q: expand using binomial theorem. (1/x -5)^4.

A: Consider the given expression as 1x-55. Below is the binomial theorem.…

Q: Question 22

A:

Q: Use Forward Gregory-Newton Interpolation formula to find a polynomial pass through the points…

A:

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

A:

Q: Fermat's theorem is true for only prime number. إختر واحداً.

A:

Q: 10 Use Binomial theorem to expand 2x .Which member contains the power x' ?

A:

Q: Use Pascal's triangle to expand thefollowing binomial expressions: 4. (1-5x)5

A: As per guideline we cab solve maximum one question ,pls repost again other question

Q: Use the Binomial Theorem to give an expression for , 210-(-3)*x10-kyk O (3x- 2y)10 O (2x - 3y)10 O…

A: See solution below

Q: Use Pascal's triangle to expand thefollowing binomial expressions: 1. (1+3x)? 2. (2+x)3 3. (1- x)3

A:

Q: 3. Determine the 4th term V2m) using the Binomial Theorem.

A: To find: The 4th term of the expression 1m2-2m5 using the binomial theorem. Formula used: The rth…

Q: 5. Use Pascal's Triangle to expand the binomial (x + 1)°. O x5 – 5x4 – 10x³ – 10x? – 5x – 1 O x5 +…

A: Given: The binomial expression is x+15. Concept used: The values of coefficient from the Pascal…

Q: (3) Determine the minimum numebber of submtervals so that sum of mtegral of nterpolatung poly-…

A: The common numerical approximations methods for integration are the Trapezoidal rule, midpoint rule,…

Q: Let ab5c be all four-digit multiples of number 36 with different digits. If someone found 7 numbers…

A: Let ab5c be all four digit multiples number 36 with different digits. As 36= 4x9, so the number ab5c…