QUESTION 3 The generating function for the sequence 1,0,1,0,1,0,1 is o a)1 +x + x2 + x³+ x+ x5 +x6+... b)1 +x2 + x4+ x6+. O c)1 + x+ x + x+ x*+ x' + x O d)1 + x2 + x4+ x6 QUESTI ON 4

Q: -, 1-, 3, 6, 12, 24 ...; find the 10th term and the sum of the first 10 terms.

A: The solution is given as

Q: Using the generating function to determine the number of ways  18 identical balloons can be given…

A: Given that 18 identical balloons can be given to 3 children such that each child receives at least 5…

Q: 2 4) The graphs of y=x and y=x make it obvious that x >x for all real number x > 1. Use induction…

A:

Q: Example/Find the nth-term of the following: 1 2 3 4 5 5'7'9'11'13' a) b) 2 4 8 16 32 0! 1!'2! 3!' 4!…

A: To find the n th term of given sequence.

Q: 1) write the mathematical expression using a) unit impulse and its shifted sequence b) unit step and…

A:

Q: За, n > 0, is n+1 ) One solution of the recursion relation an+2 = a) a2k+1 3*a1 k>0 2*k! b) a2k+1…

A: We have to find the one solution of recursion relation.

Q: 5-(1,5.25, 125.62s,3125)

A: Given,

Q: (a) 1,2, ..., 16, i.e. such that the sum of all numbers in each row, each column and each diagonal…

A:

Q: Consider a sequence of integers defined recursively as follows: a) r1 = 2, b) r+1 is divisible by…

A: Given: Consider a sequence of integers defined recursively as follows: a) x1=2 b) x2n +1 is…

Q: In R, with the code below: We create a new object a as a numeric sequence (1, 2, ..., 10), and a…

A: R is free software that is very useful for statistical analysis.

Q: You may be familiar with the formula for the sum of a finite geometric progression: if a and r are…

A:

Q: a) Solve the following recurrence relation an =8a,-2 -16a,-4 + 2" %3D

A: Question: Solve the recurrence relation an=8an-2-16an-4+2n   (Solving first question as per our…

Q: 1 5) Show that 7. diverges. + + + +

A: In this question we have to prove the series is diverges.

Q: The generating function of the sequence 4,4,4,4,4 is

A: # To find generating function of sequence  4,4,4,4,4,4 ??

Q: S1 = {1,5,25, 125 ,625 ,3125} S2 = {5,11, 17, 23,29,35} S3 = {1,25, 49, 221,169, 289, 3124} S4 =…

A: The solution is given below

Q: Prove that for all natural numbers k, a (4^k - 1)/3 + 2*a*4^k is of the form 1 + 6a

A: We show that the question doesnt hold for a=1 and k=1

Q: Prove the following using a direct proof.  If a,b, and c are integers such that b is a multiple of…

A:

Q: 1.- Let x* be defined as one more than the number of digits in the integer x. For example, 150* = 3…

A: topic - linear equation in one variable

Q: Prove that there exists an n ∈ N such that 7 | (3^n − 1).

A:

Q: One solution of the recursion relation an+2 = n+I» n 2 0, is n+1 » a) a2k+1 = (-1)*a 2k k! k 2 0 b)…

A:

Q: 8) Let a 3-2 +45 for n-0, 1, 2, 3,... If we write an as a recursive relation, it is Hint: calculate…

A: 8) Given an=3.2n+4.5n for n=0,1,2,3,...   To Find: an as recursive relation

Q: Find the number of ways that the numbers 1, 2, ..., 12 can be arranged in a sequence…

A: Observed that each sequence contain 1st 6 elements in descending order and remaining 6 elements in…

Q: 1) A, = 0, 1, 1, 2, 2;, 3, 3;, 4..; find the 40h term and the sum of the first "21 terms.

A: Nothing

Q: The generating function for the sequence 1,0.1,0.1,0,1 is 3)1 +x + x + + x+ x5 b)1 +x2 - 4. )1+ x+ x…

A: generating function is a way of encoding an infinite sequence of numbers (an) by treating them as…

Q: 1. Prove that for all numbers of k, (5*2^(2k+1) - 1)/3 is an odd number.

A: Let the given statement is        For k = 1 we get this as    is an odd number…

Q: If a₁, a2, a3, a4 are the coefficients of any four consecutive terms in the expansion of (1 + x)",…

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.