Use Gauss’s trick to determine H(n) = 1 + 5 + 9 + 13 + … + (4n – 7) + (4n – 3) + (4n + 1) I'm stuggling to know how many to multiply the sum by 2H(n) = (4n+2) (?) Is it n or n+1 or 4n+1

Q: Given this example: n-1 i. E(n – k)2* Answer for (c.i): 2"+1 – 2 – n k=0 If S is the sum, then 2S –…

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Q: What is the product of the following? (x-5)2 O x2 – 10x + 25 O x2 + 10x + 25 O 22 – 25 O a2 + 25x –…

A: From the given problem: x-52 Now we can write as: x-52=x-5·x-5 Applying the distributive property:…

Q: а (x²*) = dx

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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: (2n)! – (2n + 1)! (2n)!

A: It is required to find out , 2n! - 2n+1!2n!  For this we use factorial properties.

Q: ƒ(5x² + 4x³ − 2x + 1)dx 이름 +2 -를 +a + C 5 2 O x5 x5 + x²-x²+x+C O 20x5 + A O 20x³ + 12x² −2+ C…

A: Given, ∫(5x4+4x3-2x+1)dx

Q: Expand and simplify. (8h +3) (7h² – 4h+1) - O 56h3 – 32h² + 8h + 3 - O 56h3 – 11h? 4h + 3 O 56h3 +…

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Q: So an = n 16 n+ 16 (n-1) 16 (n-1) + 16 = n - 16 n+ 16 I X 11 (n + 15) (n + 16)

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Q: (2+i)(1+3i) – 2+ 4i= 3i O 4+2i O 3+i O 3-i0

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Q: 4.) -8n + 4(1 + 5n) %3 -бп — 14

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Q: 8n+5 II (1+i) = k=1

A: To find ∏k=18n+51+i:

Q: (f) The sum of the squares of the odd integers between 0 and 100.

A: Explained below

Q: +6n +3 is Θ (n)

A: 1st expression is TRUE

Q: Prove that: n² + 3n 1 →> 2n² + 1 2 You may use any results from lectures, but you must state them…

A: (.) Given,                We find the limit.

Q: Which simplified choice will result in 200m20n15

A: Consider the following expression…

Q: "Co 34 "C, "C, "C; (-1)" "C, ,ne Nis equal to 10 14 (4n + 2) 2" n! 2"-n! () 3.5-7...(2n - 1)(2n +1)…

A: We have use binomial theorem  1-xn=nC0 - nC1 x + nC2 x2  + .........+(-1)n   nCn

Q: 6x-1 If Зх +7 was written in the form 2+ 3x+7 then b%= (1) -1 (3) 12 (2) 7 (4) -15 21 3. 4.

A: Given  6x−13x+7

Q: (x+2)(x+ 1) y = 2x-4 (2x +3)(2x – 4)– 2(x² + 3x + 2) (2x – 4)? O a.

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Q: h(n) = 4n – 1 g (n) = n² - n Find (h o g) (4n)

A: Consider the functions  h(n)=4n-1g(n)=n2-n

Q: (-1)n+13n (b) n5n n=1

A:

Q: Which of the following is a false statement? In the expansion of (a +b) the coefficient of a b° is…

A: We have to choose the false statement.

Q: Is 12n + 18 equivalent to (2n + 6) (n + 3) ? True O False

A: Answer: True.

Q: 12 + 4j express both (a) – and (b) z +- in the form x + yj. If z =- 9- 7j ... (Simplify your answer.…

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Q: 3y CC) (2x)*(3y)"-i = Зу - (2х + 3у)" 2x n n E)(2x)-'(3y)"-i+1 %3D %3D 2x i=0 i=0

A: A polynomial containing two terms is called a binomial. To expand the binomial a+bn, use the…

Q: Which expression is equal to E (2" + n²) k-1 n=2 O (2" + n?) +D ¬k-2 (2" + n2) n3D2 nk-2 O (2*-1 +…

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Q: Make n the subject of the equation s=n/2 (2a+(n-1)d)

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Q: ( 9x2 4 if a 2 Let p(x) = 4x + 8 if a < 2 Compute the following values. (a) p(1) = (b) p(2)

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Q: Factor x – 36 O (x – 36) (x + 36) O (x + 6) (x – 6) O (x – 6)2 O (x + 6)²

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Q: 2. (a) Show that for all integers n ≥ 0,32n-1 is divisible by 8. (b) Show that 2n -1. (d) Show that…

A: Let's go through each part one by one:(a) Show that for all integers  is divisible by 8.It can prove…

Q: hich of the following expressions are equivalent to 2n 4n2 + 4n n+ 5 4n2 + 6n 10 (n+ 1) C 4n (n+1)…

A: given,

Q: 1+2 - 2x2 + (P₁ +P+1) 2"

A:

Q: Part 1. Obtain a solution to the following differential equation valid near the origin: 1.] For the…

A: Part 1. Given equation is y''+3xy'+7y=0   4. To Find: The recurrence relation for n≥2   5. To Find:…

Q: 2 + 4 + 6+ . . . + 2n = n(n + 1)

A: On solving this we will get

Q: 8 For which values of mis x - 1 a factor of x³ + m²x² + 3mx + 1? (a) Show that n = 1 is a root of…

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Q: n+2n Show that represents an integer Vn EN.

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Q: 8a2+9+1 Simplify the following rational expression: 2+3z+2 2-2 (8z + 1)(z + 1)² (x – 2)2 (8x + 1)…

A: To simplify

Q: 5. Simplify the following expressions. a) 3x + 2(5x –7) b) –8n – 8(-4 – 2n) c) k + 1 – 4(2k – 9) -

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Q: 5n (f) n10 n=1

A: