How many zeroes are at the end of 1000!/(500!500!)?

Q: Show that there are infinitely many primes.

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Q: plz solve q4

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Q: 2. Prove that " The sum of two odd numbers is even: using direct proof.

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Q: Prove that the hundreds digit of n20 is even.

A: To Prove that the hundreds digit of n20 is even.

Q: Prove that Master Cheng has won precisely 21 times in a row during some consecutive days.

A: Please find the solution

Q: How many 3-digit positive integers exist that when divided by 7 leave a remainder of 57

A: 3 digit positive integers start from 100 and ends with 999. Least positive 3 digit integer which…

Q: Show that there are infinitely many primes of the form 4k + 3.

A: We have to show that there are  infinitely many primes of the form 4k+3.

Q: Find the number of positive integers X smaller than 12849 which have exactly 2022 positive divisors

A: Theory : Total no of divisor of a number, If its prime factorization, given by ∏i=1hpiai Where p is…

Q: How many positive integers less than 850 are multiples of 8, 3, or 5? Use the Principle of…

A: Using the Principle of inclusion/Exclusion, the formula for A∪B∪C can be written as:…

Q: Show that the sum of the cubes of the first n positive integers is (n(n + 1)/2)^2

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Q: The diagram below shows ten circles joined by five lines with three circles Place all the…

A: Requirements: Numbers should range from 1 to 10.   Every line has three circles.   3. The amount for…

Q: Show that a number with 30 digits cannot have more than 100 prime factors.  

A: Prime factor: A factor of a number which is a prime number. For example: consider a number 26. The…

Q: A sequence of positive integers starts with one 1, followed by two 2s, three 3s, and so on. (Each…

A: Given:     The sequence is:     1,2,2,3,3,3,4,4,4,4,5,5,5,5,5,6,... To get this number, we have to…

Q: 3. Show that the weighted arithmetic mean of first n natural numbers whose weights are equal to the…

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Q: Use the ertended pigeonhole principle to show that there is at least 15 ways to choose 4 integers…

A: Extended Pigeonhole Principle:      If there are n pigeons and m pigeonholes and n>m. Then, there…

Q: 2"-1 for positive integers n.

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Q: Show that if any eight positive integers are chosen, two of them will have the same remainder when…

A: Pigeonhole Principle- If n items are assigned to m containers, and m<n,then at least one…

Q: Prove that the summation of three odd integers is odd.

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

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Q: Which positive integers less than 20 are relatively prime to 20?

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

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Q: Find the sum of the positive even integers up to and including 50.

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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: What two nonnegative real numbers with a sum of 23 have thelargest possible product?

A: we have to find the two non negative real number with a sum of 23 which will have largest possible…

Q: Suppose that the number of bacteria in a colony doubles every year. Set up a recurrence relation for…

A: Given that the number of bacteria in a colony doubles in a year. That is Doubles in 8760 hours.

Q: (4) Prove that there is no smallest positive real number.

A: I have to prove that there is no smallest positive real number . Suppose that there is a smallest…

Q: Show that there are infinitely many prime numbers.  0 /∈ N. (zero is not an element of natural…

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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: All Fermat's number is clearly odd numbers

A: Fermat number.

Q: A positive integer n is called superperfect if ơ(ơ(n)) = 2n Show that if n = 2q, where 2q+1 - 1 is…

A: Given: A positive integer n is called superperfect if σσn=2n and n=2q, where 2q+1-1 is prime. To…

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

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Q: Show that for n ≥ 3, ô(n) is even.

A: We have from the definition of Euler ϕ function: ϕ(1)=1 and ϕ(2)=1 Now Let n ≥ 3

Q: is there integer that has reminder of 2 when its devided by 5?

A: There are infinite number of integers that has reminder of 2 when its divided by 5

Q: sum of two even integers is even

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Q: The sum of any two integers of the from 4k + 1 is always: Even O prime Zero Odd

A: If a number n is not divisible by 2 then it is an odd number.  If a number n divisible by 2 then it…

Q: Find the average of the first 50 natural numbers is……………….

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Q: Use binomial theorum to expand (1 + 1/x)^7

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Q: Find odd and general

A: Given,       f(x)=x-π3;   0≤x≤π

Q: Fermat's theorem is true for only prime number. إختر واحداً.

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

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

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Q: 5 divides n -n whenever

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Q: the sum of any positive integers that is less than 30

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Q: Fermat's theorem is not true for some prime number. اختر واحد

A: False