find the sum of all integers between 300 and 800 that are exactly divisible by 14

Q: plz solve q4

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Q: Show that in a sequence of m integers there exists one or more consecutive terms with a sum…

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Q: Show that the sum of all  odd  integers between 1 and 1000 which are divisible by 3 is 83667

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Q: What is the smallest positive integer n such that 80325 divides n!

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Q: Let n be a positive integer. Show that in any set of n consecutive integers there is exactly one…

A: Let us take any set of n consecutive integers starting from kn+t:…

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: Any integer greater than 1 that has other positive factors besides 1 and itself is also known as O…

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Q: Prove the formula for the sum of the first positive integers:

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Q: Show by induction that if (n) is a positive integer, then ((n^3) - n) is divisible by 6.

A: Given statement is

Q: Show that an integer N is divisible by 9 if and only if the sum of its digits is divisible by 9

A: Let a=anan-1...a3a2a1 be an integer and S be the sum of the digits. Consider a,…

Q: Prove that the sum of any three consecutive numbers is divisible by 3

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Q: Find how many positive integers with exactly four decimal digits, that is, positive integers between…

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Q: How many triples of integers from 2 through 16 can be formed in which the integers are in increasing…

A: Any triple of integers (i, j, k) with 2 ≤ i ≤ j ≤ k ≤ 16 can berepresented as a string of 15 – 1…

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: Compute the sum of all integers between 60 and 150 that are exactly divisible by 8.

A: Consider the given range of number 60 to 150

Q: Show that for all n:  ceil(n) = -floor(-n)

A: In the given question we have to prove that ceil(n)=-floor(-n) That is…

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: Use mathematical induction to prove that any amount of postage that is an integer amount greater…

A: We have to prove that any amount of postage that is an integer amount greater than 53 cents can be…

Q: Determine the smallest integer that can be expressed as a sum of two primes in three different ways

A: Let us have smallest prime numbers  are, 2,3,5,7,11,13 17,19.....

Q: find all possible three-digit numbers that are of the form 75_ and are divisible by both 3 and 2

A: Since the number is divisible by 2 and 3, it must be divisible by 6.

Q: Compute the sum of all integers between 40 and 100 that are exactly divisible by 3.

A: Compute the sum of all integers between 40 and 100 that are exactly divisible by 3.

Q: noosing a positive integer from 100 to 999, what is the poSSibility of choosing a positive integer…

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Q: Use Fermat's Theorem to show that n 13 - n is divisible by 2730 for all n.

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Q: 6.) Find the sum of the first 50 positive integers ending in 6.

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Q: (b) Find the sum of the first 110 positive odd integers.

A: Our Aim is to find the sum of the first 110 positive odd integers.

Q: Find the sum of all integers that are multiples of 3 from 4 to 100.

A: We have to find the sum of all integers that are multiples of 3 from 4 to 100 Then, If A denotes the…

Q: Show that n-lis divisible by 8, if n is an odd positive integer

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Q: 1)How many integers between 1000 and 2000 are divisible by at least one of the integers 3, 5 and 7?

A: Introduction: In mathematics, integers are the sum of positive and negative numbers. Integers are…

Q: Use mathematical induction to show that given a set of n + 1 positive integers, none exceeding 2n,…

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Q: show that every integer greater than 11 is the sum of two composite integers

A: We need to prove that  every integer greater than 11 is the sum of two composite integers.

Q: Find the sum of all positive integers, from 5 to 1555 inclusive, that are divisible by 5.

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Q: find the sum of all even intergers less than 1000 that are exactly divisible by 7

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Q: Find how many positive integers with exactly four decimal digits, that is, positive integers between…

A: Note : According to our guidelines we can solve only first three subparts and rest can be…

Q: Find the sum of all even integers from 10 to 500

A: Sum of all even integers from 10 to 500 .

Q: Q7. How many positive integers not exceeding 100 are divisible either by 6 or by 10?

A: As per our guideline we are supposed to be answer only one question you can repost other questions…

Q: Determine the number of ways a computer can randomly generate one or more such integers from 1…

A: There are 5 prime numbers between 1 to 12 . Which are 2 ,3 , 5, 7 , 11.

Q: Find how many positive integers with exactly four decimal digits, that is, positive integers between…

A: The positive integers between 1000 and 9999 is calculated as follows.

Q: compute the sum of all integers between 60 and 110 that are exactly divisible by 7

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Q: The sum of all positive integers less than 400 which are divisible by 5.

A: Positive integers less than 400 which are divisible by 5 are⇒n=79 5,10,15,20,...,395 The above…

Q: (6) Find the sum of the integers for 7 to 508 Tmelusive,

A: first term (a0) = 7last term( an) = 508,     d = 1 ( natural no.)first we have to find total no of…

Q: how many perfect numbers are there between 1,000,000 and 9,000,000

A: Given- The numbers between 1,000,000 and 9,000,000. To find- The perfect square number between the…

Q: How many integers from 1 to 99,999 contain exactly two consecutive 1s?

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Q: 7. How many positive integers between 100 and 999 inclusive are divisible by 7?

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Q: Show that in any collection of 7 or more natural numbers there are ALWAYS TWO numbers whose sum or…

A: In the given problem we have to show that in any collection of 7 or more natural numbers there are…

Q: Find the sum of all  natural numbers between 250 and 1000 which are exactly divisible

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Q: Find the sum of the divisors of 120. Generalise the result for an arbitrary natural number M

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