DISCUSS: Powers of Factorials Which is larger, (100!)'" or (101!)00? [Hint: Try factoring the expressions. Do they have any common factors?]

Q: Use the Binomial Theorem to find the third term in the expansion of (3x - 2)°. The third term is|.…

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Q: Consider a population that grows according to the recursive rule Pn population Po 70. Then: P₁ = P₂…

A: Given resursive rule:- Pn=Pn-1+55 and P0=70 To find:- P1P2PnP100

Q: 's Little Theorm and The Pollard Factorization Metod how could I solve Quetion 4 in Section 6.1

A: Introduction: The product of consecutive integers beginning with that natural number and ending with…

Q: Forming Numbers How many three-digit numbers can beformed using the digits 0, 1, 2, 3, 4, 5, 6, 7,…

A: Given, To evaluate how many three digit number can be formed  using 1,2,3,4,5,6,7,8,9

Q: 10 Use the Binomial Theorem to find the eighth term in the expansion of (x- 3) The eighth term is…

A: Binomial expression problem.....

Q: Using mathematical Induction Principle 2. If 2 is a factor of k2-k+2 then 2 is a factor of…

A: 2 is a factor of k2-k+2.  That is, k2-k+2=2m,   where m∈ℤ

Q: Using the Pascal Triangle and the Binomial Theorem expand the expression (p-2q)^4

A: Concept:

Q: List four (4) properties of binomial experiments and give two examples of such experiments.

A: Binomial distribution is a type of discrete distribution, in which the variable is the number of…

Q: Еxample 7In how many ways you can draw 5 Spade cards in a regular deck of cards, if the drawn cards…

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Q: Gaussian integers has the same strength as the set of natural numbers N.

A: We need to use the fact that Gaussian integers is isomorphic to Z×Z

Q: Activity 3: Find Me! To further strengthen the foundations in solving permutations, you may search…

A: 1) the covered walk of a school is to be lined with flags. how many different arrangements are there…

Q: Q. 1 a) What is the relation between Binomial theorem and Pascal's Triangle. b) Find out the fourth…

A: Note:We are allow to answer only one question at a time. for other question please resubmit the…

Q: e the binomial formula to find the coefficient of the p term in the expansion of (2p-2)-.

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Q: Using Pascal’s Binomial Theorem, expand and simplify the following. Show all working out: (x+y)5

A: Topic = Algebra

Q: the sum. the tile pattern below, the first block arrangement has 1 block, the second block…

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Q: 4. Find the largest value of n such that 2"|16!.

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Q: n a b=1

A: The combination formula to prove the given relation is nr+nr-1=n+1r. Break the summation of the…

Q: Using binomial coefficient and Pascal triangle, compute (a + b)5

A: According to our company policy, we are supposed to answer only one question ( first or first three…

Q: a) Write down the first term in the expansion of (x - 4)5 [Hint: Care is needed with the negative 4]…

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Q: 3 of 36 > * Text-to-Speech 3. The product of two binomials, u(x) and v(x), is a binomial of degree 8…

A: Suppose, u(x) = (1+x)⁴ and  v(x) = (1-x)⁴  So, both u(x) and v(x) have degree 4 each. The product…

Q: If Pn denotes the predicted number of speeding tickets during the year 2012 + n, then Write the…

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Q: 14) You will likely want to have a calculator handy for this question. a) Create several three-digit…

A: a Let, number be 321so, 321-123=198                        =2×99Let another number be 794so…

Q: 13. Choose the best answer. The principle means if a single event has m choices and a second event…

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Q: 28. Proving a Factorization Show that x + y is a factor of -1+ yan-1 for all natural numbers n.

A: Let the given statement be P(n)             P(n) = x2n-1 + y2n-1We check P(n) for n=1 P(1) =…

Q: Consider a population that grows according to the recursive rule Pn = Pn-1+35, with initial…

A: Use the given value of P and evaluate the rest value .

Q: 2. What role do binomial coefficients play in a binomial expansion? Are they restricted to any type…

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Q: (4) positive integer n is composite without actually factoring n. Then use this method to show that…

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Q: a [The periods of recurring decimals] Let p be any prime other than 2 or 5. Explain why the cycle…

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Q: gcd(n+1, n) =

A: To Find gcd(n+1,n)=?

Q: 7. Use the binomial theorem to show E- 34 ) = 4". k=0

A: Remember, the summation form of binomial theorem is given here.

Q: Part A. Choose a and b, two whole numbers that are relatively prime, meaning that the numbers share…

A: part A two whole numbers which are relatively prime a = 89 b = 97 a and b both are whole numbers and…

Q: 2 ) Hint: Count two 2. Give a combinatorial argument to show that = n: k=1 ways the number of ways…

A: Solution is in next step

Q: a. Using the General Binomial Theorem find the power representation of(1 + x)¾.

A: As you post multiple question according to guideline only solve the first one.

Q: In the expansion of a binomial (a + b)" the third term is equal to 56, the fourth term is 70, and…

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Q: In the binomial theorem expression, what is the value of n?   A     The value of n is not needed to…

A: We have to tell what is the value of n in the binomial theorem.

Q: How many permutations are there of the letters in the following word, if all the letters are used…

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Q: Using Wilson's Theorm, Fermat's Little Theorm and The Pollard Factorization Metod how could I solve…

A: We have to find the remainder when 7·8·9·15·16·17·23·24·25·43 divided by 11.

Q: the sum. In the tile pattern below, the first block affangement has 1 block, the second block…

A: Please see the explanation below

Q: Use the Binomial Theorem to find the fourth term in the expansion of (3x – 2)°. The fourth term is…

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Q: 8 2. (1 - 3x)², (1-4)" a are three binomial expression. a. Expand 1st expression. b. In the…

A: We know that (a+b)n=nc0an+nc1an−1b+nc2an−2b2+nc3an−3b3+⋯⋯+ncnbn and general term of binomial…

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

A: Binomial expansion

Q: 18 Write the fifteenth term of the binomial expansion of (z- q°) * The fifteenth term is

A: topic - binomial theorem

Q: Consider the binomial identity () n +2 1 n n + 3 +..+n 3 = n2"-1 a. Give a combinatorial proof of…

A: Solution

Q: Prime factorization of 21

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Q: (a) Find an expression for the answer which is the sum of three terms involving binomial…

A: How many triangles can you draw using dots below as vertices? (a) Find an expression for the answer…

Q: . Use Pascal's triangle to expand the binomial expression (1+x)^3 2.Use the binomial theorem to…

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Q: Discrete Mathematics: Prove that every prime number greater than 3 is either one or more or one less…

A: We need to prove that any prime number which is greater than 3 is either 1 more than or 1 less than…

Q: Example 1 How many ways you can arrange the letters in the word STRIKED if repetition is allowed?…

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

Q: 12. (a) State the Binomial Theorem. (b) Use the Binomial Theorem to expand (x + 2). (c) Use the…

A: Binomial Theorem is the expansion theorem applied to obtain the value of the terms of any…