Q1// Let Ai be even permutation in Sn. Then O(An)=n!/2

Q: Let 8 = E--), Compute Sy for N = 1,2, 3, 4. Let S = n+2 n=1 Find S by showing that 1 3 SN = 2 1 N +1…

A: The nth term of the series is Tn=1n-1n+1.

Q: 2 le students have appeared in test a in which the top 3 will get a prise. How mony posible ways are…

A: 1.To find: the number of ways such that 3 persons get prize out of 10 persons. Please post the…

Q: 2) Find the expression for F(z) while solving the recurrence relation 2yk+2 - 3yk+1 +7yk = kak by…

A: Given: Let us consider this as equation (i) 2yk+2 -3yk+1+7yk = kak

Q: (b) Use mathematical induction method to show that 품(주-)- (두-0) (주-)-(-)1 n+1 2n

A:

Q: A box contains five cards with even numbers and seven cards with odd numbers. If two cards are drawn…

A: Given : n (even) = 5 n (odd ) = 7 n (total) = 5 + 7               = 12 number of cards drawn with…

Q: 1nnd the x-iner and yitro tn caumon. Then gopn we conon uing grapining poper snon Oution

A: Note: We'll answer the first question. Since the exact one hasn't specified. Please re-submit the…

Q: 2) Set up the de finite imtegro gain bat u- substitution and then evaluate it,

A: Evaluate by applying u substitution

Q: 10. Show that for all n E Z, n² – 3n +1 2.

A: Use mathematical induction to prove the given statement. Check whether the result is true for n=1.…

Q: n2 +2 2 3n for n = 1,2,3,.

A:

Q: 2- Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 =x(2n + 1) P-n Pn-1

A:

Q: What is the correct solution of the recurrence relation an = 6an-1- 9 an-2 , Wwith initial condition…

A: Given,          The recurrence relation an=6an-1-9an-2 , with initial condition a0=2 and a1=9.

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

A:

Q: It can be shown that C, the average number of com- parisons made by the quick sort algorithm…

A: Consider the provided question, Here, we have to solve only part (a), because in part (b) mentioned…

Q: Jse strong induction to prove that if n E N and n > 10,

A: Base step for Strong induction

Q: nl diverges because an > 0, for all n 2 1. ) True False

A: Given statement is

Q: Find f (n) when n = 3k, where f satisfies the recurrencerelation f (n) = 2f (n∕3) + 4 with f (1) =…

A:

Q: (b) Let Ho =1, H1 =3, H2 =9, and define Hk = Hk-1 + 3Hk-2 + 3Hk-3 for k23. Show by induction that Hk…

A: We will prove the result by induction  H0=1≤30 H1=3≤31 H2=9≤32 The result is true for k=0,1,2 Assume…

Q: THEOREM 2.4 The number of distinct permutations of n things of which n1 are of one kind, n2 of a…

A: Given: Theorem 2.4 and Theorem 2.5

Q: 2. Prove that |µ(n)| _ S(s) S(2s) n=1 if s > 1.

A: Riemann zeta function is a complex-valued function defined as ςs=∑n=1∞1ns.  There is a relationship…

Q: Calculate the coefficient of x7y5zx7y5z in (x+y+z)13(x+y+z)13. (b) In her discrete math class,…

A:

Q: Prove that for every non-negative interger n: 2n+1 + (-1)" Σ 3· 2n i=0

A:

Q: Find the solution to the recurrence relation an=5an-1, n>=1 with initial condition ag= 1.

A:

Q: 4- From the generating function, prove the recurrence relation: 2n Jn-1(x) + Jn+1(x) In(x)

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Q: Prove T(n)= 2T(n-1)+n can be in 0(n2")using represented telescoping method

A:

Q: Now, from the relations in (6) we get Wn = µ+ kn (Wn-1 + Wn-2) and zn = € + Vn (žn-1 + Zn-2). (9)…

A:

Q: (7) Let S = {1- (-1)" | neN}. Determine inf S and sup S. Justify. n

A: To find inf S and sup S .

Q: If C and D are two n ×n invertible matrice hen one of the following is always correct

A:

Q: 1 ient of in al</z] <2 is

A:

Q: 1. Prove that {2" : n E Z} = {,n :n E Z}.

A:

Q: 7. Prove that 2. O = (-1). %3D

A:

Q: Compute Li(Ni – 2) dt O-4 0-2 None of these

A: Given, ∫-11t13-2dt We have to compute the integral.

Q: (7) Let S = {1- (-)" | n € N}. Determine inf S and sup S. Justify. n

A: To find the supremum and infimum of the sequence S .

Q: 2- Use Eq. (1) to prove the recurrence relation: (n + 1) Pn+1 = x(2n + 1) Pn - n Pn-1

A:

Q: 2. Generate six random numbers by using Congruential or Residual Generator.Xi +1 ≡ (aXi + c) (mod…

A: 2)   Given that,   Xi+1=(aXi+c)(mod m)   Here,   a=5 X0=3 c=1 m=8

Q: 6. What sequence of pseudorandom numbers is gener- ated using the linear congruential generator xn+1…

A: Given: Linear congruential generator xn+1=4xn+1 mod 7, with x0=3 To find: Sequence of psedorandom…

Q: 6. Use mathematical induction to show that, Vn > 7, n! > 3".

A:

Q: 5. Prove that for all n EN sufficiently large, 3" > 2n² + 1.

A:

Q: Let n ∈ Z, Is it true 4 | n4 – n? Prove it or counterexample.

A:

Q: 5. Previously we used the recurrence relation dn+1 = 0.5dn + 200, d₁= 200 and the assumption that…

A: Given dn+1=0.5dn+200 and dn→L as n→∞. To find L .

Q: Find f (n) when n = 2k, where f satisfies the recurrencerelation f (n) = f (n∕2) + 1 with f (1) = 1.

A:

Q: 1c ical induction to prove 11

A:

Q: Q1// Let Ai be even permutation in Sn. Then O(An)=n!/2 إضافة ملف

A: Question 1) Sn denotes the set of all permutations of n objects. Then, |Sn| = n! &amp;, An denotes…

Q: Exercise 7. Let {an}1 and {bn}-1 be {an + bn}=1 diverge to -o and {an · bn}-1 diverge to +o.…

A: Let k&lt;0 be any given real number. Since an→-∞, there exists n1∈ℕ such that an&lt;12k, for all…

Q: 4. Prove that the L{2t²} = 4 S3

A:

Q: 1. For In 5n2 + 9n3 + 1, ɑn =n², prove or disprove: In O(an) (n → ∞)?

A: Given:  xn =5n2 + 9n3 + 1, αn=n2. we have to prove or disprove : xn =O(αn ) ( n→∞).

Q: What is the solution to the recurrence relation: Tn=5nTn-1+6 with T0=3?

A: We will find out the required solution.

Q: 9:Let S [o,1] Prove that inf s=o

A:

Q: 8. Following the idea of Exercise 6 and referring to Exercise 7, express the positive gcd of 49,349…

A:

Statements and Logic

Logic is the analysis of general patterns of thoughts without regard to any specific sense of context.