Prove n k Vnk €N+, Σ (Í[6+5)) = i=1 Here, the meaning of II is j=0 n II = ¹ 1.2.... i=1 .n k+1 1 k+2 ][(n+i) i=0

Q: 8.) What is the distance between an airplane flying at 120 feet above sea level and a turtle…

A: We find the distance between an airplane flying at 120 feet above sea level and a turtle swimming at…

Q: Let P(x) = 2x² – 5x – 12 = (1 – 4)(2a +3). Which of the following is true? O A. For 1E[-2/7, 1),…

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Q: 4 A. Given M= 0 1 5 i. iii. MN 0 4 and N= -5 3 Det (M) 6 0/ MT-2N (T means transpose) 3 5 -4 5 -2.…

A: According to bartleby guidelines we supposed to do the first three sub parts of multiple sub parts…

Q: 10. Give a combinatorial proof: For n ≥ 1 and k ≥ 1, (n)k = n · (n − 1)k-1.

A: To give: A combinatorial proof: For n≥1 and k≥1, k·nk=n·n-1k-1.

Q: HW 2: If Z - N(0,1), find a) p(Z > 1.2) b) p(-2 <Z< 2) c) p(-2 <Z < 1)

A: If Z~ N(0,1)   which means clearly it is standardized normal distribution table.

Q: 27 Find (all) the value(s) of c such that 3c" n= (A) c=3 (В) с— 4 (C) c = - (D) c=} 33 %3D (E) с 3…

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

A: Here we have a given equation that

Q: )(2n) for conplex number sequance show that if lm En=1 then 3no fN such that for for Hn 7 no o Znto.…

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Q: 18 16х + 17 dx Evaluate

A: ∫xndx=xn+1n+1+C where n≠-1

Q: Verify by o Mathematical Induction dt todt E (2-1) = n²(2n²-1) for alt nz!

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Q: 133. -Σ 2" Sn+ -(x + 2)" n=0

A: Consider the series, Rewrite this as Now take the constant outside,

Q: -4 M" = -127 14 Let M = 6 Find formulas for the entries of M", where n is a positive integer.

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Q: 15 Σ (3k +2) K=11   (Find Sn)

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Q: Let m, n 1 be integers. We have

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Q: 10. Show that È k(C) = n2"-1. Using Combinatorial Proof. k=1

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Q: 9. dx 64+x2 Evaluate O 9Tt 8 оп 9Tt 8

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Q: 1 О. 15 Show that %3D (D - Q) k e k

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Q: {[(B U C)U A] N [(B UC)U A]}n {[(A U B)UC] nÃ}

A: We use the following properties of set operations: Distributive law: (A∩B)∪C=(A∪C)∩(B∪C)…

Q: How make that? k = (5²+1) JK ds = (5+1-15+0·1) ·10 (115²-185-11) (105²+115+1)²

A: Step 1: Given K=−(s2+1.1s+0.1)(s2+1)​. To Find: dsdK​ Step 2: We know that if f(x)=v(x)u(x)​, then…

Q: Which of the following is TRUE? 2x2+1is n(x2) since Cx222x²+1 for all x 21 where C=3. OA. n is a (n3…

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Q: [2 Define A = 1 -2 Lo ܚ ܨܢ ܝܪ -12 31 5 0 -2 -2 1. Evaluate, showing your work: (i) B = (ii) (iii)…

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Q: Let gcd(a, b) = d then which of the following is correct (i) (ii) b|d (iii) d|(ax – by) v[p a. All…

A: gcd(a,b) = d  So, by definition, d | a and, d | b  &amp;, d | (ax - by) for all integers x &amp; y…

Q: (15 – b) (9 – b) - z = 6. 6. För a = 1 och b + 3 saknar systemet lösningar. För a = 1 eller (4t) , y…

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Q: Show that 2"=nCk and 0 = [(-1)^nck k=0 HINT: Consider(1-1)" and (1+1)" k=0

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Q: 3. Compute |(1+ i)(1 – i)(1 + 3i)| .

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Q: Find a particular solution of the equation y4 -y3 - y" - y' - 2y = 8x^5:

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Q: Σ s2 an convergent or divergent?

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Q: (1 2 43) 32 1. IF A = THEN (A) (B) (X Y) Z W

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Q: 8 Σ 26 2(5 Find: k=1

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Q: Compute gxxyz for g(x, y, z) = x7y6z6. (Use symbolic notation and fractions where needed.)

A: We have to find  using given data.Concept required:While finding partial derivative of  w.r.t. , we…

Q: Prove E-1(4i – 3) = n(2n – 1) for natural numbers n 2 1. i=1

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Q: 3. Prove that 6|(9" - 3") for all n E Z+.

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Q: Evaluate L{cos² 3t} s² – 18 a) s(s² + 36) s2 – 18 b) s(s² – 36) s² + 18 c) s(s² + 36) s2 + 18 d)…

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

A: To prove:We will use mathematical induction to prove this.Let

Q: _. . Prove that z² = + Emo(-1)" (n + 1) (²2)", where |z-21 < 2.

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Q: (i) in n(n+ 1) r = r=1 (ii) n(n+ 1) (2n + 1) 6. r=1 (iii) in 2. n(n+1)]2 3

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Q: Starting with y= In(x3) 2 T 2,3. %3D

A: To find: The derivative of y=lnx2+32π. Given: The function is y=lnx2+32π. Concept used: Logarithmic…

Q: find following timia the exist Pim 1t y ス→。 fim (2'tyo) In (xty?) ()

A: For a function f(x) the expression limx→af(x)=b means that the function tends to value b when domain…