Show that 8(-n--8()

Q: plz solve q4

A:

Q: Find § 6-42 (Z+3) by Residue Theorm.

A: We have to evaluate the integral ∫ 6-4zz2z+3dz using the residue theorem. For this, we have to find…

Q: Show that 1+2+3+...+n= ("""). (";"').

A:

Q: In the expansion of + 6)-", state the number of terms and the coefficient or the middle term. 21, 20…

A: Introduction: The binomial expansion is a very important finite series in mathematics. With the aid…

Q: Pigeonhole Principle Prove that among any 100 integers there always two whose difference is…

A: The given problem is to prove the following statement which follows the pigeonhole principle, we…

Q: 6. A. Show that 81 – x²dx : 81n %3| 4

A: According to company rule we can answer only first question and rest can be reposted

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

A: 20510-75

Q: Prove by mathematical induction

A: The principle of mathematical induction is a technique or method that is used to prove the statement…

Q: Use mathematical induction to prove that +1+2+4+...+2"-² = 2"- for all 2 -- positive integers . п.

A: We need to prove using mathematical induction given statement First we will show statement holds for…

Q: Prove that for all integers, n , n^3-n is divisible by 3.

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Q: Use the definition of an r-permutation, or the product rule to de number of trifectas possible in a…

A: Given: To explain the given statement as follows:

Q: Determine all minors of  A = [ -8   6   3 ]        [ -9   9   2 ]        [ -7   9  -5 ]

A: Given the matrix   A=-863-992-79-5

Q: . Show that n! > 3ª for n> 7.

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Q: Show that 3n^ 2+8nlogn is big-Oh (n ^2 )

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

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Q: Show that 1/n - 1/(n+2)= 2/(n(n+2))

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Q: Show that (n + 1)!)" < 2! · 4! - (2n)!.

A: The objective is to prove the given statement using induction

Q: Derive an expression for the sum of the first n positive even integers.

A: We Use the A.P series. Find The sum of the first n positive even integer.

Q: How do we proof that 2logn = n?

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Q: Prove that for any 9 consecutive natural numbers, there exists one number that is prime to the other…

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Q: Find: The sum of all positive integers less than 400 which are not divisible by 5.

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Q: Suppose 50 cars start at a car race. In how many ways can the top 3 cars finish the race? The number…

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Q: In 3 - In x - In(x + 5) = 0

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Q: What is the coefficient of x^4 in the expansion of (-1+ x)^11

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Q: how to prove √6 is irrational

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Q: Prove that AXB|=A²B² - (AB)².

A:

Q: 5. Give a recursive definition of the set of positive integers that are multiples of 5.

A: Solution

Q: Prove 3√3  is irrational

A: See the attachment.

Q: Find the sum of those integers between 1 and 500 which are multiples of 2 as well as of 5

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Q: 2. Show that if a]b then a'|b² for all integers a and b (Symbols V, 3, A, V, V,A,→,-)

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Q: Show that (n + 1)! > 2"+3, for n > 5.

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Q: Show that there are no prime triples other than 3, 5, 7.

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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: If a and b are integers with gcd(a, b) =d Then gea (-) -- gcd

A: False

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: Prove (n + 6)² – (n + 2)² is always a multiple of 8. (Use direct proof.)

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Q: Show that n! > 3ª for n > 7.

A: The given inequality is, n!&gt;3n We need to prove that, the inequality is true for n≥7 Firstly,…

Q: Show that n! > 3 for n ≥ 7

A: We have to prove this assertion that, n! &gt; 3  for n≥7 We will prove this statement by the method…

Q: Suppose 26 cars start at a car race. In how many ways can the top 3 cars finish the race? ..... The…

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

A:

Q: how many positive integers n satisfy 22-5n>-3?

A: 22-5n&gt;-3

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

A:

Q: Give a recursive definition for the set of all the positive integers that are less than 100 and not…

A: Given: Set of all positive integers that are less than 100. To find: Recursive definition for the…

Q: 4. Use a combinatorial argument to show that () n 1 -2) n + 22 n 2 3 -

A: Given: nn-2=n3+12n2n-2n

Q: Which term of the expansion of (x + 7)° contains x° Term number contains x°.

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Q: sum of two even integers is even

A:

Q: Show that 5 | n5-n for all integers n.

A: To prove the above statement we will use the principle of mathematical induction which is divided in…

Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π

Permutations and Combinations

If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.

Counting Theory

The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.