Find the sum of the first 50 odd natural numbers. Find the sum of all the even integers from 12 to 864, inclusive. Find the sum of all the odd integers from 27 to 495, inclusive.

Q: Find the greatest natural number n such that n + 10 divides nº + 100.

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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: Two-digit natural numbers are formed, with replacement, from the digits 0 through 9. How many…

A: We know that two-digit natural numbers are formed with replacement, from the digits 0 through 9. To…

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: If n is an integer, then 2n + 1 is odd

A: Given , n is an integer We have to show that 2n+ 1 is odd

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: Find all integers n such that (n^2) - 1 is prime.

A: n² - 1 = (n-1)(n+1)  Now, if (n² - 1) needs to be a prime, then, either n-1 is equal to 1 or, n+1 is…

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

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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: The integers 77 and 105 are relatively prime. صواب İhi

A: By finding the factors of given numbers you can find the solution :

Q: How many numbers between 1 and 10000 have the digits 1,3, and 5 such that each digit appears exactly…

A: Here Numbers between 1 and 10,000 have digits 1,3,5 and each appears exactly once only

Q: Let Sbe the set of all (nonnegative) 4-digit integer. How many integers from start with 1 and end…

A: let S be the set of all 4-digit integer. how many integers from start 1 and end with 9

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

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Q: 4. Find all the prime numbers that can be expressed in the form n2 – 9 for some integer 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: Find the sum of the odd integers between 228 and 60

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Q: 27. Determine the number of n-digit numbers with all digits odd, such that 1 and 3 each occur a…

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Q: Find the sum of the first 100 positive odd integers.

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Q: Find the sum of all four-digit numbers that can be formed by the digits 1, 3, 5, 7, 9 without…

A: Answer: Option b)  666600

Q: 5. Given a real number x and a positive integer k, how many multiplications are used to find kx by…

A: Given,A real number x and positive integer kTo find: Total number of multiplications used with the…

Q: (a) Suppose that there are k distinct positive integers that divide an odd positive integer n.…

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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 integers from 10 to 500

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

Q: Assume that all four-digit integers (numbers from and including 1000 to and including 9999) are…

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Q: How many positive odd integers less than 10,000 can be written using the digits 3, 4, 6, 8, and 0 if…

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Q: Every natural number has a successor every number except 1 has a predecessor

A: We know that  Successor  is that number which can be find adding 1 in the given number  So if we…

Q: If n is a positive integer, is there always a prime between n and 2n?

A: given that n is a positive integer. we have to show that there is always a prime number between n…

Q: Consider all numbers between 20000 and 70000. Efficiently determine: A) How many of these numbers…

A: Part A - Let’s represent the number as ABCDE. You have to considere the special cases first, since…

Q: Find the least natural number a with the property that the sum a + 2a + 3a + .. + 9a is the number…

A: Given sum is  a+2a+3a+4a+5a+6a+7a+8a+9a

Q: 2 6. The sum of the first n odd natural numbers is equal to n.

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Q: (5n)! Prove that 40"-n! is natural number for every natural number n.

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Q: The number of primes of the form n³ – 1 is 1) 1 2) 2 3) Infinite

A: To choose correct option

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

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Q: How many integers between 100 and 999 have distinct digits, and how many of those are even numbers?

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

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Q: How many can 3 digits be formed using the digits from 1 to 5 if the digit 2 is never there in the…

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Q: 1- The total number of positive integers that can be formed from the digits 1,2,3 and 4 if no digit…

A: NOTE- AS PER POLICY I  HAVE CALCULATED FIRST MAIN QUESTION ONLY. Here Given 4 digits 1,2,3,4

Q: For each natural number n, if 3 does not divide (n² + 2), then n is not a prime number or n = 3.

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

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Q: Find the sum of the integers from −20 to 256.

A: It is required to calculate the sum of integers from -20 to 256 that is:

Q: Find the sum of all integers from 41 to 83. The sum of all integers from 41 to 83 is

A: Detailed Solution and Explanation is given below....

Q: Two-digit natural numbers are formed, with replacement, from the digits 0 through 9. How many…

A: Given that two-digit natural numbers are formed, with replacement, from the digits 0 through 9. So…

Q: Find the sum of all natural numbers n such that 2021-n/99 is a natural number ?

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

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Q: What is the sum of odd numbers from 1 to 501. 2. Find the sum of the first 50 even numbers.

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Q: 55. the sum of the first 80 positive integers 56. the sum of the first 120 positive integers

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Q: Show that 19 divides 10*8n-1 + 33n-1 for every positive integer n.

A: Concept: Mathematical induction: For each and every natural number n, mathematical induction is a…

Q: How many four-digit positive integers both start and end in even digits:

A: We need to find the number of positive integers both start and end in even digits.