Prove that if k

Q: Show how series is divergent

A:

Q: Suppose you draw n lines in the plane so that every pair of lines cross (no lines are parallel) and…

A: Let n be the number of non parallel lines. Given that number of regions= Rn Let Un represent maximum…

Q: Rationalize the denomi 20 5/10 - 7/5

A: 20510-75

Q: Find functions defined on the set of nonnegative integers that can be used to define the sequences…

A: For (a), Given: Here, the sequence is f(n)=(-1)n+13n+1 for each n∈ℕ.

Q: Suppose that {an}----->a, convergent real number sequence. Prove that {can}---->ca, for every c…

A: Suppose that {an}----->a, convergent real number sequence. Then, We have to prove that…

Q: Use sigma notation to write the sum.

A:

Q: Find the sum of the first 21 positive integers. The sum of the first 21 positive integers is

A: We will use the concepts of A.P.

Q: Show that for any k > 3, any tree with a vertex of degreek must have at least k leaves. The proof…

A: Suppose there are l < k leaves. The degree of each leaf is 1. Let there be n vertices. There is…

Q: Use generating functions to determine the number of differentways 15 identical stuffed animals can…

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Q: Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i.…

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Q: A finite sequence of numbers is called AWESOME if each subsequent member of the sequence, except the…

A: Find the product of already given natural numbers. To make the product of all four natural numbers a…

Q: Let n and k be positive integers with 2k + 1 ≤ n. Find the number of ways to choose k children from…

A: Consider the given: Let n and k be positive integers with . Choose the number of ways in which k…

Q: Explain how to expand (a + b)' using the binomial theorem n an-kbk. Be specific. k expression, k-0

A: Given:      a+b7 The binomial theorem:        a+bN=∑n=0NNnaN-nbn where Nn=N!n!N-n!

Q: Prove the z-transforms for common sequences summarized

A: So as per as our guidelines i am supposed to answer only 1 question please repost remaining part

Q: Find Exponential Family 4-{N(0,1),0 € (-∞,+∞) }

A: Dear student, If you find this solution helpful please upvote ? it.   Here in this question it has…

Q: Poove 4 is an upper bound of f2,4) also poove sup (2,4)= 4

A: To prove that 4 is an upper bound of (2,4) and Sup (2,4)=4. Definition:1 Upper bound : Let S is a…

Q: How many bijective functions have [10] as both the domain and codomain

A: Given, 10

Q: prove that "The Sum of two odd numbers is even: using direct. Note:- 1 want the ansawer on a paper.

A: The sum of two odd numbers is even. Proof :          Properties odd and even integer.          If…

Q: Prove that sequence {an}= {(-1)n} does not have a limit.

A: According to the given information it is required to show that {an}= {(-1)n} has no limit.

Q: z = -2 verify that |7 - 2| < |||| - |||

A: Given that y¯=−310 and z¯=1−21. We have to verify y¯⋅z¯≤y¯⋅z¯. Now y¯⋅z¯=−310⋅1−21=−5 Hence, y¯⋅z¯=5…

Q: Suppose I claim that the average age of all students at college is  24 years.  a) Express Ho and…

A: Given, we have claim that, the average age of all student at college is 24 years a) The hypotheses…

Q: Suppose real sequences (sn) and (tn) are bounded. (That is, that their ranges are bounded sets.) i.…

A: Since sn and tn is bounded then there exist some finite reals Us,Ls,Ut and Lt such that:  Ls≤sn≤Us…

Q: Prove: “The sum of two even integers is even.”

A: To prove: The sum of two even integers is even. n is an even number if it can be expressed as n =…

Q: Show that — ф+1 n=0 ||

A: Given φ is the golden ration satisfying 1φ=φ-1. To prove ∑n=0∞1φn=φ+1 It is known that φ=1+52.

Q: Use quantifiers to express the associative law for mul- niplication of real numbers

A: The associative law for multiplication of real numbers using the quantifiers is

Q: Find the recursive and explicit rule for -1, 3, 7, 11,... Recursive rule

A: This is a problem of series . Based on concepts and formulas we will answer the question.

Q: Find the recursion for a population that doubles in size every unit of time and that has 14…

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Q: Use generating functions to determine the number of differentways 10 identical balloons can be given…

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Q: Use a combinatorial argument to show that n 1(n 3 |

A: The LHS of the expression is nn-2. This is the number of ways selecting n-2 objects from n objects.…

Q: combinatorial proof

A:

Q: Show that N-, (x) = (-1)"N„(x). Nó(x) = -N1(x). with open steps and explained pls

A:

Q: 16. Find the positive integer that maximizes the sum of the numbers and its reciprocals?

A: Take integer and add them with his reciprocal Diifferenciate and get

Q: 8. Find Za/2 for a = 0.04.

A: Given, α = 0.04 α/2 = 0.02 Zα/2  is value found by z value corresponding to probability 1-α /2…

Q: In binomial if g(x) =0, then

A: Given:  gxnx=0                                        (1)

Q: Suppose I claim that the average age of all students at college is 24 years. a) Express Ho and Ha…

A: Given Information Claim : - Average age of all students at college is 24 years a) Null and…

Q: Suppose that a1, a2, a3, . .. is a sequence of sequences of zeros and ones. aj is a11, a12, a13, ·…

A:

Q: countable in number, such that

A: Given : W=Iα:α∈A is a collection of open intervals, then there exists a sub-collection , say Ii :…

Q: Suppose 7 female and 6 male applicants have been successfully screened for 5 positions. In how many…

A:

Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π

Q: Draw a number line on which adjacent tick marks are 0.1 unit apart and on which 0.003 can be plotted…

A:

Q: Define Permutation and Combination in your own wo

A: Permutation is a way to arrange the given objects or numbers in order .

Q: A decimal string is a string over the alphabet of the 10 characters: {0, 1, 2, 3, 4, 5, 6, 7, 8, 9}.…

A: Given that a decimal string is a string over the alphabet of the 10 characters 0,1,2,3,4,5,6,7,8,9.…

Q: Write a recurrence relation that describes the sequence 1, 1,3, 3,5,5, 7,7,9,9, .... Don't forget to…

A: We will find out the required recurrence relation.

Q: Find the sum of the first 80 positive even intergers.

A: Sum of the arithmetic progression with for n terms where a1 is the first term and an is the last…

Q: Find two positive integers such that the four times loo0 and the product large as possible. the .…

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Q: d the image of the point (-2,4) under the expansion with factor 2 in the direction. ) (2,8) (-2,8)…

A: Given query is to find image of the point after expansion.

Q: Suppose 10 people are potential candidate of a conference (the number of people invited to the…

A: From 6 graduate student 4 can be selected in 6C4 ways, and for undergrad students they can come with…

Q: Explain what is important about monotonic and bounded sequences.

A: A sequence is said to be monotonic , if it is either monotonically increasing or decreasing. A…