n factorial

Q: 2. Find non-recursive (i.e. just regular) formulas for the following sequences: (a) 5, 2, -1, -4,…

A: A non recursive formula is a formula for a sequence that does not itself depend on any other terms…

Q: Use sigma notation to write the sum.

A: Given sum is: 21+3n23n+...........+21+3nn23n We have to write the sigma notation for the above sum.

Q: al .avil of aanwemo bit of zhasn The binomial (13 - 5y)nlog2128 is expanded and fully simplified. If…

A: Using the properties of the logarithmic functions, it can be written that: log ab=blog alogaa=1…

Q: Find the first six terms of the recursive sequence. a1 = -3, an = an-1 + 8 %3D O -3, 5, 13, 21, 29,…

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Q: Fermat's theorem is not true for composite number. Select one: O True O False

A: Ans :  true

Q: Use mathematical induction to show that n people can divide a cake (where each person gets one or…

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Q: 6 points What is the fourth term in the binomial expansion of (2r– y)? |

A: We have to find fourth term in the binomial expansion of 2x-y7. We know rth term in binomial…

Q: Use sigma notation to represent the sum of the first seven terms of the following sequence 4,10,16

A: Given sequence, 4,10,16,... To find the sigma notation for the first seven terms of the sequence.

Q: 4. What is the equivalent recursive definition for am = 12 + (n- 1)3? ||

A: Given,         The equivalent recursive definition for an=12+n-13.We know that,         The general…

Q: A sequence {am} is called increasing, if an > an+1 for all n > 1. Select one: O True O False

A: We can answer it as below as per the definition of increasing function.

Q: a. Assume that nothing is known about the percentage of passengers who prefer aisle seats. n= (Round…

A: a. The percentage of of passengers who prefer aisle seats is not known consider as 0.5, 99%…

Q: 24. Give a recursive definition of a) the set of odd positive integers. b) the set of positive…

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Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: 25 Evaluate the sum: 4k²) - k=1

A: Explanation of the solution is given below..

Q: How do you determine how many terms there are in a binomial expansion?

A: In the binomial expansion a+b2 ,  The expansion obtained is  a2+b2+2ab. In the binomial expansion…

Q: Use sigma notation to write the sum. 2-4+8-16 + 32-64 Σ

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Q: In(n)

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Q: 3. Consider the word PERMUTE and all the ways you can arrange its letter using each letter only once…

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Q: Show the recursive function for the following sequence.......... 2, 5, 8, 11, 14..........n.

A: Here the sequence is 2,5,8,11,14,.......... We have to find the recursive function.

Q: state the recursive formula that generates the last number in the sequence 1, 2, 3, 5, 7, 11, 15,…

A: The given sequence is 1, 2, 3, 5, 7, 11, 15, 23, 31.

Q: In n

A: Given as, an =Innn3

Q: Use induction to prove the summation formula п(п+ 1) Σ holds true for all n € N. Hint: In inductive…

A: Mathematical Induction is a special way of proving things. It has only 2 steps: Step 1. Show it is…

Q: noosing a positive integer from 100 to 999, what is the poSSibility of choosing a positive integer…

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Q: Use the binomial theorem to prove that 2^k * "n choose k"  =. 3^n.

A: Binomial theorem: The statement of binomial theorem is given below:

Q: The sequence n-21 is divergent. True False

A: We have given a sequence  ,   n-2. We need to determine sequence is convergent or divergent. We know…

Q: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: b Explain how every recurring decimal with an infinite string of 9s can be written as a terminating…

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Q: what is the notation in sequences? Expaln it.

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Q: Evaluate the factorial expression. (n+ 2)! n!

A: The evaluation is as below

Q: Evaluate the factorial expression.

A: Given:               n+2!n!   n+2!=n+2×n+1×n×n-1n-2........3×2×1 n!=n×n-1n-2........3×2×1

Q: Give a recursive definition of Binomial coefficient () in terms of (") (we assume n2 k). Do not…

A: The objective is to give the recursive definition of Binomial coefficient  n+1k+1 in terms of…

Q: A. Express in factorial form: a) 7x6х5x4x3х2x1 с) 4x3x2x1

A: Given that 7*6*5*4*3*2*1 11*10*9*8*7*6*5*4*3*2*1 4*3*2*1 13*12*11*10 We have to express in…

Q: Find the value of the factorial. 7! 7! = (Type a whole number.)

A: In this case, we need to find the value of factorial of 7.

Q: 2. Derive the following binomial identity: (n + () --("-") = r

A: To derive the binomial identity; n+1rn+1=rr-1n We have to prove that the left hand side of the…

Q: how that the sequence (1 – (-1)" +1/n) is divergen

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Q: d. If the chosen sequence has a finite number of terms and its sum i are there? e. Express the…

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Q: Use sigma notation to write the sum. 5 5 5 4 + 1 4 + 2 4 + 3 4 + 12 Σ

A: By using sigma notation to write the sum.54+1+54+2+54+3+...+54+12

Q: Prove Γ (n) = (n-1)! where n ∈ ℕ

A: Concept: The proof for this gamma integral will be done using mathematical induction

Q: Evaluate Factorial Notation 200! 197!

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Q: (n + 6 )! n+6

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Q: Use sigma notation to write the sum. 61 3 1 3 + 2 3 + 3 3 12 12 6 6.

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Q: Use Mathematical Induction to show that 52n -1is divisible by 8,   ∀ ∈ n N.

A: Use Mathematical Induction to show that 52n -1is divisible by 8,   ∀ ∈ n N.

Q: n that includes all terms up to

A: The initial value problem is , w''+7xw'-w=0. It is given that w0=6, w'0=0. w''+7xw'-w=0. To find the…

Q: Find the sum of all natural numbers n such that 2021-n/99 is a natural number ?

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Q: se mathematical induction to show    n ≥ 0, 7n - 1 is divisible by 6

A: Given: n≥0, 7n-1 To prove: 7n - 1 is divisible by 6

Q: Which recursive rule describes the sequence 3, 7, 11, 15, ... ?

A: First we have to find out 1st term and common difference.

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

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.