4 i. 9-n+24n+1 n2 + 4n + 3 n=1 2n + 1 ii. > n²(n + 1)2 n= 4 iii. と2+3n + 2 n=2 |

Q: )"-( 18 6. lim V n4n +(4n)" 2+ n2 4 4+ n2

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Q: (-1)*+1 1 = 4 ) 2n – 1 n=1 = 4 -+- + - 8.

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Q: Determine whether or not the infinite series below converges.

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

Q: The sum of n,2n,3n terms of an AP are S1,S2,S3 respectively.Prove that S3=3(S2-S1)

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Q: D. Show that if a, = 3n³ - 17n² + 2n - 6, then an O(n³).

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Q: 1UT) 117 If the sum of m terms of an A.P. is equal to the sum of either the next n terms or the next…

A: We have to prove the given expression using the given information of arithmetic progression.

Q: 8n and IfΣ (ακ+ be) - n+1 k-1 2(ak - E(ak - br) = - n, then ak = n+2 k-1 k-1 3 O 2 9. m/2 2. wwwwww

A: simplify the equation by adding them and tends to limit to infinity.

Q: (n^2-n)+((n-1)^2-(n-1))+....+(1^2-1) =n(n+1)(2n+1)/6 - n(n+1)/2

A: We shall first derive the formulas for sum of first n natural numbers and sum of squares of first n…

Q: IfΣ ( a+ bk) 4n_ and n+1 k-1 E(ar – br) +, then Ear n n+2 k=1 k-1 2 O None 2 2

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Q: fΣ (α + bk)- 6n and n+1 k-1 (ak- br) = 1 = then ar - n+2 k-1 k-1 O None 3 5. O 2

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Q: n If E (ak + bk) 2n and n+1 k=1 E(ak – br) +, then ak = n n+2 k=1 k=1 3 2 5 2 O None 2

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Q: 4. Conclude that n2 n=1 ||

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Q: n-1 For all n > 2, 4+ 3n4" – 4n+1 - j=1 9.

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Q: IfΣ (aκ + bk) 6n and n+1 k=1 n Σ (α- bk) then Lar = n+2 n k=1 k=1 5. 2 None 3. 2

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Q: 5) Suppose that W1 < R" and W2 4 R". Prove (W1 n W2) < R"

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Q: Determine whether the following is true: (a) (b) n+1 Σ₁2²= n · 2n+² + 2, i=1 n i-0 3¹ 1- 3n+1 13…

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Q: 1)What is the numerical result of n! a) (n – 3)! = n(n – 1)(n –- 2) %3D | " ()-() - (3) 25 %3D 6. 10…

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Q: Fix k, n E N with n > 2 and k <n – 2. Prove that: | )-(".) · ) (:) ) (^) = (":") 2 + k 2 n – 2 n n +…

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Q: It is known to be Q-N. Accordingly, show that QxQ ~ N.

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Q: 2.5. Let 1, 0sns9 0, elsewhere and h[n] = { 1, 0sns N 0, elsewhere x[n] %3D where N s 9 is an…

A: Since you have asked multiple question, we will solve any one question for you. If you want any…

Q: 2n if 1sn< 457 | Зп +1 b) {a,} where a, ={ne"* if 457 <n< 2100 4n –1 if n22100 5n+7

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Q: For any positive interger n, (n + 1)! / n! - n = (A) 0 (B) 1 (C) n (D) n + 1 (E) n!

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Q: IfΣ (aκ + bk) 8n and n+1 k=1 Σ (α- br) then ak | - n+2 k-1 k=1 None 3. 2. 2.

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Q: that Edn H(n/d)7(d) = 1 and Edn H(n/d)o(d) = n for all n, where r(n) = d(n) and σ(n) = σι (n) Σm d.…

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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: . Show that if an = 3n3 - 17n2 + 2n - 6, then an = Θ(n3).

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Q: 14. If n e Z, then 5n2 +3n + 7 is odd. (Try cases.)

A: By method of direct proof, prove the statement " If n∈ℤ, then 5n2+3n+7is odd"k∈ℤk∈ℤ as follows.

Q: (-1)"(2n–1) Σ n(n– 1) n=2 IM:

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Q: 2. Given ON=4x NE = 3x +8 OE = 36 36 %3D 0 4x N 3x+8 E ON + NE = OE

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Q: If (ar + bx) 8n and n+1 k=1 n Σ (α- br) 1 1. then ar n | n+2 k=1 k=1 O 2 None 9. 2 5 2 3 2

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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: μ1 = μ2 = 0, n2 = 27 and n1 = 19; thus df is:

A: Given that, μ1 = 0, μ2 = 0, n1 = 19, n2 = 27. df is degrees of freedom for testing the hypothesis,…

Q: c) Suppose that Y ~ N(2.08,0²) with P(Y > 2.2)=0.274. Find o. Andaikan bahawa Y ~ N(2.08, o²) dengan…

A: We have to find sd.

Q: (-1)" In(nº) Σ 20. 4n n=2

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Q: 4) (n* + 12n² + 37n² + 21n – 27) ÷ (n+ 3) |

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Q: 4 a. En=1 100 3n3-5n 11 b. nylnn n=1 3n! С. Z1·4·7·10 … (3n + 1) ... n=0 8

A: See the details solution in below

Q: f m: n=5:3, find 3m +4n : 6m -2n

A: If m: n=5:3, find 3m +4n : 6m -2n

Q: Q.8 Í xPn+1®n+2dx= Evaluate: n+1*n+2° -1

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Q: Select the correct comparisor 1 Σ n=1n2 +5 Select one: a. Non of them b. Σ 2" n =1 C. n2 n = 1 d. Σ…

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Q: solve for t

A: Given equation: eln2t=12

Q: ъ) n EN COn n > 0, (2n)! < 22n . (п!)?

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Q: Given: 21 = 2 23 = L4 e || n Prove: 2 3

A: …

Q: 8. Ση-0 ne-1 4n 9. En=0 (n+2)3 n=0 (n+2)³ 3. 10. Σ0 n-3n+2 %30 n2-3n+2

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Q: Vn EZ, if n+5 is odd then n is even

A: This question is related to integer values. We can prove it by using direct or indirect way. Please…

Q: that d | n + 5 and d | n2 + 7, then d | 32. , then n + 5 and n2 + 7 are coprime.

A: For part (a) We have to prove that d is an integer such that dn+5 and dn2+7, then d32. It is given…

Q: 2. n+ 3 п — 14 n +1 п? — бп — 16 + n? – 4n – 32 - | n? + 6n +8

A: The given equation is: n+3n2-6n-16+n-14n2-4n-32=n+1n2+6n+8

Q: If Σ (a bk) 4n and n+1 k=1 Σ ( a-bk) n+2 1, then Lar = k=1 k=1 5 2 None 2 2 3

A: Series

Q: Is 2 (n² + 6n + 9) equivalent to (2n + 6)(n + 3)? O True False

A: (1) Function ht=15+60t-16t2 Given that value t=10…

Q: Since n.n=1 and n-n2=(2/2)/5 then n3 +3/5 %3D

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Q: 3 n2 + 9n + 18 n=1

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