10 Evaluate Σ(2n – 1). n=1

Q: n = n and n = 1. n Show that in

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Q: solve 5.3 (using k(pi-k)/2) and setting k =pi/2 or by your own methods if you have easier ones

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Q: P(X₁ = x₁, ..., Xn = xn) = P(X₁ = x₁) [I²²2 P(X; = Xi| X₁ = X₁, ..., Xi−1 = Xi−1 )

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Q: Σ n=1 (n+2)(n+3) ОА. 1 О в. 1 4 Ос. 1 2 %3D

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Q: 15 Σ (3k +2) K=11   (Find Sn)

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Q: TL ( - k) = | k-1 a. 6n + (n + 1)(2n + 1) - b. n(n + 1)(2n + 1) c(n²-1) C. O d. n3 e. 00 f. 플 (n +…

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Q: n (n + () A k=0 | B, = 0.

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Q: Prove n (2k – 1) = n² - k=1 for every n EN.

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Q: Alireza will take IE 4301 next semester and attend EVERY class in person. He will wear a mask to the…

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Q: 16) n = 4; 2, 1 and 3 + 3i are zeros; f(1) =78 %3D

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Q: 8. Determine (MN)-1 where M (:) 5 and N -5 2

A: The given matrices are M=8541  and  N=5-1-52. Evaluate MN as follows.…

Q: Show that for any n E N, 7(15".

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Q: Show that n 1 i2 i=1 <2 - n

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Q: If Z ~ N(0,1) what is P(-0.83 < Z < 1.06):

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Q: ind all solutions for n EN for which P(n, 4) = 12P(n, 2).

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Q: Let n = WEE 5 Find n - 1. n – 1 =

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Q: Show that for any n E N, n(n + 1)(2n + 1) k=0

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Q: Transform the following sum by making the change of variable j =i-3. Here, n23 is an integer. 2 – 4i…

A: We use the given relationship between i and j to transform the given sum.

Q: Let P(A) = 0.3 and P(AUB) = 0.7. For what value of P(B) are A and B independent? O4/7 1/4 O 1/3 O…

A: Given: P(A) = 0.3P(A ∪ B) = 0.7

Q: 4. Show that inf {1+ ¼n: n EN} = 1 %3D

A: I have proved that the sequence is decreasing and convergent.

Q: Show that for all n e Z, n? – 3n +17 2. -

A: Given: For all n∈ℤ, n2-3n+1≠2

Q: Find all n such that σ(n) = 72.

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Q: Prove that n Sk k=1 = n(n + 1)(2n + 1) 6 for all n € N.

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Q: 1 E(-1)". n(n+ 4) n=1

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Q: Show that, for n > 1 2n 1.3.5... (2n – 1),2n 2.4.6...2n n

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Q: 10 Determine the exact value of Σ(2k2 – 3). - k=1

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Q: Prove n 2 2n 1 k = n k - 1 n k=1

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Q: Σ(0) - i=0 n Σ ;*² (1) = (n + n?)2n-2. n2n-1

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Q: Prove that Σ₁ iª = n(n+1)(2n +1) (3n² + 3n − 1) i=1 30

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Q: 2y 2 Given that 7* ×49' = 1 and 5x x125 3 1 calculate the value of x and of y. 25

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