Let n eN 1. Show that o (n²) = ng(n) 2. Show that o (n) +

Q: Describe in words the region of R' indicated by the inequality: 1sVy² +z? <4

A: Given inequality is, 1≤y2+z2≤4.

Q: To show that the general factorial function: (a)= mn (-). (+¹).(+-¹). here m is a positive integer…

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Q: . How many Boolean functions are there of degree 7? Explain.

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Q: 10. Use induction to show that 1x2 + 2x3 + + n(n+1) = " for all n € N.

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Q: determine the value of c(n,5) /p(n,5) where n can be any integer thats 5 or greater

A: Recall the following. Permutations Number of permutations of n things taken r at a time: pn,r=n!n-r!…

Q: . Show that n! > 3ª for n> 7.

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Q: Prove C(n,0)=C(n,n)=1 for all whole numbers n

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Q: Is it possible to find a number  n  such that is ∫0∞  xn dxconvergent?

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Q: (c) Prove that for n ≥ 1, n [27/7/2≤2- j² 1 n

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Q: Let w be defined as 2 more than the number of digits in the integer w. For example, 15 =4(2 digits…

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Q: Show that (n) ‡ 14 for all n ≥ 1.

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Q: 00 8tan-in Zn=1 n3D1 1+n2

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Q: Prove an+1 = (an2+ 1) / 2 with a1 = 2 is monotonic increasing.

A: Solution:-

Q: Let X-N(65,36) P(x> 55) = O 0.5232 none O 0.9525 0.98077

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Q: Show that any positive integer n with n ≥ 4 can be expressed as n = 2x + 5y where x ≥ 0, y ≥ 0.

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Q: b) Evaluate UTM L{t*e- 6(t-2)}. TM

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Q: Let D = {2, 4, 8) "For every z D, 2x¹ €

A: Given that set D = { 2, 4, 8}  And statement is  " For every x in D,   2| x". We need to check that…

Q: Let X-N(65,36) P(x<70)= O 0.50798 none O 0.98077 O 0.76973

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Q: Prove:  C(n,k) = C(n-1,k-1)+C(n-1,k) for natural numbers k with 0<k<n.

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Q: Write the recursive definition for an = pn n! where a1 = p.

A: The recursive formula is used to describe the relationship between two terms of any sequence. The…

Q: Let I be ar. V. has a Binomial dist. B(n,@) with the Pid.f. fex; G)o-0^,X:o,n Show that fex;)…

A: Given that X is a random variable which has binomial distribution Bn,θ with p.d.f is given by:…

Q: Evaluate |P(A)| if A={n: n is a prime number from 1 to 100}

A: To evaluate : PA if A=n : n is a prime number from 1 to 100

Q: Show that. 1 (n + 1)(n + 2) n=1

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Q: Define the Fibonacci numbers as Fo = 0, F₁ = 1 and for n ≥ 2, set Fn = Fn-1+Fn-2. Show that Fn+1Fn-1…

A: Let's prove the identity Fn+1Fn−1−Fn2=(−1)n for n≥1 using mathematical induction.Base Case (n =…

Q: Show that for any integer n ≥ 2, C(2n,n) > C(2n,n-1)

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Q: Show for all n ≥ 4 that n² <2n.

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Q: For each integer n>1, let A(n) denote the sum of the integers from 1 to n. For example,…

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Q: Prove that for n 2 2, F²r-1-F²n= Fn-1 Fn-2 Where F, denotes the nth Fibonacci number.

A: Facts:F0=0F1=1F2=1F3=2F4= F3+F2=2+1=3etc.Fn = Fn-1 +Fn-2

Q: Let Fn denotes the nth Fibonacci number, where F1 = F2 =1. Which of the following is true about Fn?…

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Q: (a) Show that if n € N, then <¹dr. n+1

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