7. (a + b)"= E=o( n choose k) a™-kb* for any integer n>=0. Use this theorem to compute (2x-3)* ) The binomial theorem states that for any real numbers a and b,

Q: 5) Prove that : tanz 올n(를) i-z

A: tan-1z=i ln[(i+z)/(i-z)]/2.

Q: u will prove that 7*+1 - 1 is divisible by 6. ypothesis, since 6 evenly divides , there exists an…

A: We will fill in the blanks.

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: Determine the term involving y5 in the expansion of (3y +).

A: Please refer the attached image for complete solution. THANK YOU.

Q: A company that packages peanuts states that a maximum of 6% of the peanut shells contains no nuts.…

A:

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

A:

Q: is divengent 2) Show that the harmoni series

A:

Q: What is the smallest integer that is a quadratic residue for all prime moduli p > 2?

A: We know if there is an integer 0<x<p, where p is a prime, such that x2≡qmod p, then q is said…

Q: Show with the help of Fermat’s little theorem that if n is a positive integer, then 42 divides n7 −…

A:

Q: Use Fermat's Theorem to find a number x between 0 and 28 with x 85 congruent to 6 modulo 29. (You…

A: as given  x85≅6mod 29   ...i as we known 29 is a prime number  by fermat's little theorem if p is a…

Q: Use Euler's Theorem to find a number x between 0 and 28 with x85congruent to 6 modulo 35. (You…

A: Here finds the value of x for which: x85≡6mod35 and x lies between 0​  to 28

Q: If there are a total of 8 chocolates be given to to three children such that each children receives…

A: Given: 8 chocolates  are to  given  to 3 children such that  each children receieves at least two…

Q: 10. Show that the interval (0, 1) is covered by the open intervals In (1/n, 1- 1/n), n 2 3, but (0,…

A:

Q: 4. Find the coefficient of the term containing x' in the expansion of (x-2y)“.

A:

Q: 4. Find the expansion of (x + y)6 using Binomial Theorem.

A:

Q: Suppose that 100 lottery tickets are given out in sequence to the first 100 guests to arrive at a…

A: given  number of lottery tickets = 100 according to question, number of winning tickets = 12 the…

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

A:

Q: 2. Suppose that the number of bacteria in a colony triple every hour. a) Set up a recurrence…

A:

Q: Suppose a, n E Z and 0 < a< n. Prove that ()- (":")- (:-) n - 1 %3D + a a а- 1 in two different…

A: Given a,n∈ℤ such that 0&lt;a&lt;n. (1) Consider:…

Q: What sequence of pseudorandom numbers is generated using the pure multiplicative generator xn+1 =…

A:

Q: Suppose that Hilbert’s Grand Hotel is fully occupied on the day the hotel expands to a second…

A: We know, Hilbert's Grand Hotel is a thought experiment which gives counterintuitive property of…

Q: 4. Suppose we are in a parallel universe where 6 dollar coins and 11 dollar coins exist. Show that…

A:

Q: Ahmet borrows n TL from Burak. Starting from today, Ahmet pays back to Burak 2 TL or 3 TL at each…

A: Given that Ahmet borrows n TL from Burak. Starting from today, Ahmet pays back to Burak 2 TL or 3 TL…

Q: 8. Show that for any orthonormal sequence F in a separable Hilbert space H there is a total…

A:

Q: Number of solutions of the equation 3x - 2x + 5x2 + x+2= 0 under modulo 5 is'are OB. OD 3

A: Consider the given equation, 3x4 - 2x3 + 5x2 + x + 2 = 0 The set modelo 5 is, ℤ5={0, 1, 2, 3, 4}…

Q: 6. Prove that ER, # 0.

A:

Q: 4) Find the Term that free from x of the expansion (x2 +10

A: Use binomial expansion:-

Q: 3. Find the expansion of (x + y)$ using Binomial Theorem.

A: The solution is given as

Q: 27. Show that if x and y are positive real numbers that have the same first n digits in their…

A:

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

A:

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator Xn+1 =…

A: Given that xn+1=(3xn+465)mod 8191x0=1

Q: Prove the fallowing egudion for every n,2 by hathematical enduelion. 35.6+35 6+ 35.63+ -+35.6"= 7.6"

A:

Q: Let X,X2 uith Parameters ----Kn bears from binomial distr'bli- n ando

A: From the given information, X1,X2,.....Xn from the Binomial distribution with parameters n and θ.…

Q: What sequence of pseudorandom numbers is generated using the linear congruential generator xn+1 =…

A: According to the given information, it is required to find the sequence of pseudorandom numbers.

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

A:

Q: 2. Show that for every n 2 2 and every 0 <k<n- 2, within the triangle of Binomial Coefficients k+2…

A: We will use properties of binomial coefficient  nCr  +  nCr-1=n+1Cr+1Note : nCr=nr=n!r! n-r!   Proof…

Q: Question 22

A:

Q: 1. Show that if seven integers are selected from the first 10 positive integers, there must be at…

A: We can solve the following question by pigeonhole principle

Q: Show that if seven integers are selected from the first 10 positive integers, there must be at least…

A: We can solve this question by pigeonhole principle

Q: Ofind an upPer bound for the reciprocaL of the modulus of ż"-52+6 if 121=2 2Itint: z" -52²+6= (2?…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: 10 Use Binomial theorem to expand 2x .Which member contains the power x' ?

A:

Q: : Use he comparism test to prove hat n-2 Converyes

A:

Q: 1c ical induction to prove 11

A:

Q: Find the first 4 terms of Toaylor Polyuocuial generated by fCx)= xlnx at a=2.

A: We find first four terms of Taylor polynomial generated by f(x)=xln(x) at a=2.

Q: 3. Determine the 4th term V2m) using the Binomial Theorem.

A: To find: The 4th term of the expression 1m2-2m5 using the binomial theorem. Formula used: The rth…

Q: 4. Prove that the L{2t²} = 4 S3

A:

Q: How many words of lengthn≥6 in the alphabet{1,2,3}contain at least two of each digit?(Prove a closed…

A: Here we have to find the total number of possible ways of length n≥6 in the alphabet {1,2,3} contain…

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

A: We will find out the required solution.