(i) Show that (r + 1)² (r + 2) – r² (r + 1) = (r + 1)(3r + 2). - (ii) Hence find (2 × 5) + (3 × 8) + (4 × 11) + ... + (n + 1)(3n + 2). (iii) Show that you can obtain the same result by using the standard formulae to find the sum of this series.

Q: EX1 FIND THE 4th TERM BINOMIAL EXPANSION (3x+2y) ³ IN THE OF 3

A: The given expression,      3x+2y5

Q: Simplify the complex fraction. n-4 -2n-15 n+1 n+3 n-4 (n- 3)(n +1) n-4 (n- 5)(n+ 3) n-4 (n- 5)(n+1)…

A: Given n-4n2-2n-15n+1n+3.

Q: %3D k (n+1) (k-10 (n+1) k +1 (*) n+1)

A: The correct option is the last option. The detailed solution is as follows below:

Q: find the 4th term of (2n^2-3m)^4

A:

Q: the coefficient of x^2n in the expansion of (1-x)^2n is

A: Hello, thanks for your question but according to our policy I am answering the very first question.…

Q: Σ The coefficient recursion relation for the solution y An xn-1 of the n=0 equation xy" + 3xy' +…

A:

Q: 2 Look at the following picture. 000 000 1st term 2nd term 3rd term Prove that the number of…

A: Given:

Q: 3x

A:

Q: The coefficient of x2 in the expansion of [1- x/2]3  -   (a + x) 4 is 2a where a>0. Find a.

A: The coefficient of x2 in the expansion of [1- x/2]3  -   (a + x) 4 is 2a where a>0. Find a

Q: 3) Find the non-recursive formula for f (n): f (0) = 6, f (n) = f (n – 1) + 15 for n>1

A: Given f(0) = 6 and f(n) = f(n-1) + 15

Q: In the expansion of ( 2x – 3y )4, find the sum of the coefficients of all the terms.

A:

Q: 1 In the expansion of px2(5+px)8, the coefficient of the term in x6 is 3402. Find the value of p.…

A: Expansion of polynomial.

Q: 3. The fifth term in the expansion of (2x + k) is equal to the fourth term in the expansion of (2 +…

A:

Q: At a bowling alley, the cost of shoe rental is $2.75 and the cost per game is $4.75. If f(n)…

A: Calculation of above requirement are as follows.

Q: i. Find the coefficient of x in the expansion of ( 2x –÷) . ii. Hence find the coefficient of x in…

A:

Q: Find the expression of 1/(2+5x)3 , magnitude of 5x/2 < 1, in ascending powers of x up to and…

A:

Q: (n - 11n +17n + 16) divided by (n– 3) n2 - 8n-6, remainder -6 n- 8n - 7, remainder |

A:

Q: 5 Given A=-2 6 0 2 92719 2, and X= x₂ show that XTAX = 27, suggest that 5X + 6X3+7X3-4X₁X₂ + 4X₂X3…

A: Solution:

Q: 2. Given that the coefficient of the term from the beginning and the term from the end of the…

A:

Q: If the sum of the coefficients of all even powers of x in the product (1 + x + x² + ... + x2n) (1 –…

A: Introduction :

Q: Find the 6th term in the expansion of (3x+2)^8 b) Find the coefficient of the x^5 term in (5x+1)^11…

A:

Q: An investigator was interested in the most effective way to teach college algebra. He assigned his…

A: Here the two groups are Independent, one is younger students and other is older students

Q: 3 divides n^3 + 2n, whenever n is a positive integer. Solve using mathematical induction

A:

Q: a) Factor  f(x)=x^3-4x^2−16x-64  into factors of the form (x-c), given that 4 is a zero. (b) Solve…

A:

Q: 2. Let, a1= 3 and for n ≥ 2, an = 2an-1 + 1, express an in terms of n. for n ≥ 3, an = 2an-1+ bn-1…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS. WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

Q: If a_1=8a1​=8 and a_n=-3a_{n-1}an​=−3an−1​ then find the value of a_4a4

A:

Q: (a) Complete k (-1)* 2k+n = -½(x) k! (k + n + 1)! k=1

A: Solution a: Given ∑k=1k(-1)kk!(k+n+1)!x22k+n=-J?(x)            (1) Since we know that…

Q: -1/2 p. Find the coefficient of x" in the expansion of (1– 4x)2.

A:

Q: HW Solve the fallowing first order 0E. -3= \-3+メー

A:

Q: A binomial distributinon with parameter n=5 satisfy the property 8P(X=4)= P(X=2). Find P left…

A:

Q: x+(x+1)+(x+2)+(x+3)+(x+4)=5x+10 What does this prove about the sum of these natural numbers?

A: The sum of the given equation is calculated as follows.

Q: The series k=1 3k (k² + 1)“ + 20

A:

Q: Question 67 Find the sum (4z2 - 5z) + (2z° - z2 + 3z) A. 6z3 - 6z B. 6z - z2 - 2z C. 2z3 + 3z2 - 8z…

A:

Q: What is the value of f(-2) of the polynomial f(x) =-a + x + 1? What does this mean about the linear…

A:

Q: 1 1 1 1 2 1 of finding the coefficients are equivalent

A:

Q: 2. the number of terms in the expansion of  ( (x+4y)^3(x-4)^3)^2 is? 3. The 5th term of from the…

A:

Q: 1. Solve the following problems by using the Binomial formula.  a. If n = 4 and p = 0.10, find…

A:

Q: 4 (a) Write out the multiplication table for Z6. How many times does [0]6 appear in each row of the…

A:

Q: 1. Show that the binomial coefficient 2"Cn is always an even number for all n > 0.

A: Here, the given binomial coefficient is: Cn2n To prove that it is always an even number for all…

Q: 1) Express the polynomial x + 2x2 - 5x + 2 in a series of Laguerre polynomials.

A:

Q: 1 Consider the expansion of (3x + p/x)8, where p>0. The coefficient of the term in x4 is equal to…

A: Explained below

Q: Suppose you are expanding (5x - 2y) a)i) How many terms are there in the expansion? )State the…

A:

Q: 10. Find term number 3 in expansion of: (4x + 2)^9. (Note, term number 1 is (4x)^9) the coefficient…

A:

Q: Please explain how the -20k is brought back into the formula, Thanks Solution c: Obtain the sum: R.=…

A:

Q: In theexpression of (x + 4y)^12, what is the numerical coefficient of the fifth term?

A: Given expression is x+4y12. To find the numerical coefficient of fifth term. Solution: General term…

Q: 1+(-3)" Find the sum of 72 4h n=0

A: Given series,                  ∑n=0∞1+-3n4n

Q: When converting repeating decimals into fractions, is it possible to sometimes get a fraction that…

A: Note: As there are two separate questions posted, we will answer the first question according to…

Q: 4 Find the coefficient of the given term when the expression is expanded by the binomial theorem…

A: Find the coefficient of x2y7 in (2x+3y)9 using binomial expression.

Q: Expenses for a company for year 1 are $24,000. Every year thereafter, expenses increase by $1000…

A: Given that expenses for a company for year 1 are $24,000. Expenses increase by 3% = 0.03 of the cost…