Suppose r is a real number such that 0 < r|< 1. 1 (a) Show that there is a y > 0 such that |r| = 1+y 1 for all n E N. ny (b) Prove that |r"| < (c) Prove that {/nx"} converges to 0. (d) Prove that, if 0 < u < 1, then {nu"} converges to 0. [IIINT: For all n, nu" = (Vnu"/2)2.]

Q: What is the coefficient of x²wa³b in the expansion of (x+y+w+a+b)??

A: To determine the coefficient of x2wa3b in the expansion of x+y+w+a+b7.

Q: 21 2. 6.

A:

Q: Using the Binomial Theorem & Pascal's Triar expand the binomial, (a - b)* A. a -4ab3 + 6a?b? - 4a³b…

A:

Q: How many terms are there in the multinomial expansion of (x₁ + x₂ + ...........+xr)n?

A: Multinomial expansion :  (X1 + X2 + X3 + ......Xr)n  We have to calculate no. of terms in this…

Q: A = 6 -2 -2 10 -3 5 1 ---3-0 C=0-2 a = 1, b = [3 08]. -10 1 . B 5 2 11 9 4 4 7 0 0 11

A: We have to solve given Questions.

Q: 12 Find the term of (a – 3b)" that has b in it.

A:

Q: Select and order the steps to prove the special product pattern for the square of a binomial. Step…

A: A square of a binomial is of the form (c+d)2  We first write it as a product (c+d)(c+d)Then we…

Q: 5/14+1/6

A: 514+16=15+742

Q: Find the coefficient of x5in the expansion of (1 – 2x + 3x2)5

A: I have solved Algebraically

Q: n?_4

A:

Q: Express the graph in Figure Q3(a) in terms of a unit step function and then find the Laplace…

A: We have to find the Laplace transform of given graph in term of unit step function

Q: 1 7. 27 2.

A:

Q: Use the sample data and confidence level given below to complete parts (a) through (d). A research…

A:

Q: Find the coefficient of x4 in the expansion of (2-3x)6

A:

Q: find  3/4 + 1/8

A:

Q: Use the binomial theorem (more than once) to expand (a+b+c)³.

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Factor 10k + 1 into a product of primes for k = 1, 2, 3, 4, 5.

A: The main objective is to factor p(k)=10k+1 into product of primes for k=1,2,3,4,5.

Q: In the expansion of (x + y)14 which term has the highest coefficient ? O a. x10y4 O b.x7y7 Oc x14 d.…

A:

Q: 4/11+3/8

A: Topic:- simplification

Q: How many terms are there in the expansion of (4.x + 7y)0.+ (4x- 7y)10 ?

A:

Q: 7. How many terms are there in the multinomial expansion of (x₁ + x₂ + ... .+x)"? ******..

A: We want to find the number of terms in the multinomial expansion of x1 + x2 + ... + xrn

Q: What is the 5th term in the expansion of (2x²y³ – ¹y)° O 14.25x7 y 20 15.75x10 y 19 15.05x¹0y17…

A: Given: 2x2y3-14y9=2x2y3-y49

Q: (3) Find the prime factorization b. 180

A:

Q: W 4. What is the value of the 4th term of the expansion (a + b)"? O a5 O 5a*b O 10a²63 10a b?

A:

Q: | (16 – 2*) dz =

A: To find : the value of ∫0216-x4dx   Using the formula ∫abxndx=1n+1bn+1-an+1

Q: Evaluabe: 25+3 se

A: Here we find Laplace inverse transform

Q: 1 3 8.

A:

Q: 4. Find the 11th term in the expansion of 25 3x + 5xi

A:

Q: Find the nth term of  (– 4 3 14 29 ) and (4, 5, 8, 13)

A: Sequence

Q: 8-12 (²

A: -83

Q: 22 7/8 - 7=

A: Given,

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.