Let r E No and n E N. In this problem, a general formula for o,(n) is found. (a) Let n e N. Prove that (ple+1)r – 1 o,(n) = II (2 p* – 1 pe||n

Q: Show that E=12n)/n! diverges. Recall from the Laws of Exponents that 2m) = (2")".

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Q: 7. 6|n(n+1)(n + 2), Vn E N

A: Given that: 6|n(n+1)(n+2), ∀n∈N

Q: (1+ In x)' - dx is a. (1 + In x}' . C - +C 5 O b. (1 + In x)* + c 3 (1+ In x)² +C 3 O d. (1 + In x)…

A:

Q: 3. Prove or disprove the given statement. (a) If x e R, and x + 0, then 2x > x. (b) If n e Z*, then…

A: Given: (a) If x∈R, and x≠0,then 2x>x (b) If n∈Z+, then 2n-1>0

Q: N-1 N, k-r = mN, m an integer | Se-i(27/N)(k-r)n n=0 0, otherwise

A: To prove: ∑n=0N-1e-j2πNk-rn=N,k-r=mN, m is an integer0,otherwise

Q: 00 Eak, |a| < 1 k=2

A: ∑k=2∞ak,  a&lt;1

Q: dx 'x(1+x³)

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Q: S In x dx = x + x In x Select one: a. In x - In|1+ In x | + C b. In x +C O C. (In x)² + C d. In In x…

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Q: Prove if equal to MPn (W) dx= 2" (n!)" (2n+)! that m is an integer

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Q: Let a, b eR with a < b. Assume that a + <b - for all n E N. Show that b- = (a, b). %3D n n=1

A: We will show  two sets are equal.

Q: If fo) = x + 1 then (/(2r)) at x= 1 O a. 2 O b. 1 Oc8 O d. 4

A: This question is about differentiation of functions

Q: S Vī dx (2/3) x3/2 + c O (3/2) x3/2 + c (2/3) x2/3 + c O none of the above

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Q: Let a, b eR with a < b. Assume that a + <b - for all n e N. Show that n n=1

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Q: The table shows the scores of two students in Mathematics and English in 2-item seatwork. Englishty)…

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Q: If A = [1 1] then the dimension of N(A) is O a. 1 O b. 3 OcO O d. 2

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Q: Evaluate (23* e dx O (2e)" + C In2e O (Be)* In8e + C (2e)* In2e + C O (8e)* + C In8e

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Q: Consider a positive integer 1 < i < 9. Then, given T(n) = 2T([n / 2] + i) + n, show that T(n) E O(n…

A: Given: T(n)=2Tn2+i+n The positive integer 1≤i≤9

Q: 7. Find the value of K, so that (x + 4) is a factor of P(x) = 2x³ + x² - kx + 20. 8. Find the value…

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Q: The evaluation of 2xe³ dxdy is 3e-1 O e-3 e-1 O None of them O -3e

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Q: Show that e = o (hª) as h → 0 for all values of q.

A: Like big O notation, there is also a little o notation. There is a difference between big O and…

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

A: The solution is given as

Q: S ze dz. |2|=1 Find

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

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

Q: Evaluate 23x e* dx O (2e)x + C In2e (8e)* In8e + C (2 e)X In2e + C (8e)X + C In8e

A: Firstly, converting the product of the two terms into a single term.

Q: Evaluate the following formula for p₁=0.9, p₂ = 0.1, P₁ P₂ = 0, P=0.374695, q=0.625305, n₁ = 46, and…

A: Given that: Sample proportions are: p^1=0.9p^2=0.1 Difference in population proportion: p1-p2=0…

Q: Show that E=1 2n) /n! diverges. Recall from the Laws of Exponents that 2(n) = (2")".

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Q: So 20 (x? – 1)ª æ dæ = O 2/5 O 20 O 2 O -2 O -20

A: Definition used -                 Definite integral -                 ∫abf(x)dx =F(b)-F(a)…

Q: The number e can be defined by e= (1/n!), where n!=n(n-1)-2-1 for n 0 and 0!= 1. Compute the…

A: For the solution of the problem follow the next steps.

Q: 2 5 2 If A= 4 6. 4 then |A| is -1 2 -1. |A|=0 |A|=1 |A|=-1 O

A:

Q: 8. Prove the following. A. Let X = {a e N|a = 3t + 4, for some t e N} and Y= {a eN | a = 21t + 4,…

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Q: (п — 1)! The expression D (In x) is equal to True False

A:

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.