81. Prove: 2+4 +6+ + 2n = n(n + 1). ...

Q: Given that the expression (n²+n+1) n! can be written as a(n + 2)! + b(n + 1)! + cn! where a, b, c…

A: The main objective is to find the sum value.

Q: (10) + 2(11)¹ (10)8 + 3(11)²(10)7 + ... + 10(11)⁹ = k (10)⁹ then k= ?

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Q: dratic equation by using the quadratic formula and, if needed, to submit your answer as a fraction…

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Q: If N=6+4+3+1+1/3N, then the value of N is?

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Q: (2)(3+1) de (22+22+3)* (3)

A: NOTE: ACCORDING TO BARTLEBY GUIDELINES, SOLUTION OF FIRST QUESTION WILL BE PROVIDED.

Q: 19. What is the value of (pk) when p is prime and k is a positive integer?

A: We know that the value of the Euler ϕ-function at the positive integer n is defined to be the number…

Q: calculate 1+3+5+...+(2n-1) for n = 1,2...,6.

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Q: Prove that 5 does not divide 5n+3 for any integer n.

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Q: What is the coefficient of x16 in (2+x³ – xª)7 ? -

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Q: (14x- 13) 4x + 13) (6x + 2)

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Q: 2- Show that: (-1)m (2m + 1)! NIE

A: Solution:     Definition of Bessel's function:

Q: 2(210) 2(510 210) 510 210 510 3 2 1 show that 1 4 2(510)210 10

A: To calculagte the 10th power of the given matrix in the required form

Q: 4 (ii) 16 | at + 15.

A: Step-1 1)16|a4+15

Q: 3) (n² + 10n+18) ÷ (n+ 5)

A: To divide the following expression.n2+10n+18÷n+5

Q: Multiply (3x-2X2x+

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Q: 2. The sum of three consecutive positive odd integers is always a multiple of (A) 3 (B)5 (C)7 (D)9…

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Q: 6. Simplify these algebraic expressions. a) 2m + 12n - 3m - Op+ 10p +m – n- 12p b) 5r+ 13t +…

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Q: 3(n+7) =  blank + 21

A: We have to solve

Q: **2.) In the diagram below, ray NK bisects JNL MJNK-(22-2 and MELNK-(3x)". Determine the value of…

A: Given: In the diagram, the ray NK bisects ∠JNL. m∠JNK=2x2-2°. m∠LNK=3x°. Since the ∠JNL is…

Q: n+1 n+3 n+ム ニ

A: To find the value of above infinite series first we will check the convergence of given series using…

Q: Show that: 15|(24n − 1) for all natural numbers n.

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Q: True or false: If a is any integer, then (5a + 2,7a + 3) =1. Justify your answer.

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Q: 37! D- Given that N= (191)(15) is an integer: i- Does the prime 11 divide N? What about the prime…

A: N = 37!19! 15!37! consist numbers that are divided by 11→11, 22 , 33→319! consist numbers that are…

Q: (b) 6 + 7 + 8 + 9 + ... + k

A: (b) Given that 6+7+8+9+...+k The objective is to find the sum. The formula for sum of numbers are,…

Q: 2) (n²-n-29) (n-6)

A: Please refer to the image below

Q: The sum of three unequal negative integers is - 18. What is the smallest possible value of the…

A: Since the three numbers are negative and unequal , to get the smallest possible value among the…

Q: i do not undertstand where the 8 has come from in q2c

A: Part c,            4log32-log34-2log33-log312

Q: Suppose that a and b are integers, c b = 3 (mod 19). Find the integer c that a) с%3D 13а (mod 19).…

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Q: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: (:)? /3 9. Which of the following is equal to (b) (–1)"-12·5., 3"n! 3.5-7..... (2n + 1) (Зп — 4)…

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Q: True or False. Briefly explain If p is odd prime then p divides 2p−1+(p−1)!.

A: Given: is an odd primeTo check:The prime divides  or not.Results used:Wilson's Theorem:For any…

Q: Use Gauss's trick to determine H(n)=1+5+9+13+...(4n-7)+(4n-3)+(4n+1) I got n(4n+2)/2 is this…

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Q: What is the product of 3 and 3?

A: To find the product of given irrational numbers.

Q: Show that n² #0 (4n²) by giving a simple argument

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Q: = (-² −4) ² (a) AB If A = -6-16 (c) 14+24 (b) BA -6-63 12-21 A² = AA 9+28 -21-42 and B = =(-²3). 4…

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Q: Is 1 raised to the power of 2 + 2 raised to the power of 2 equal to 3 raised to the power of 2?

A: