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

Q: 2. Find six rational numbers between 3 and 4

A: We can solve the given problem using concept of rational numbers which is, Therefore d=(y-x)/(n+1)…

Q: The sum from k=1 to infinity of: [(5sin2k)/k!]

A: Given,

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

A:

Q: 19. What is the value of (pk) when p is prime and k is a positive integer?

A: We know that the value of the Euler ϕ-function at the positive integer n is defined to be the number…

Q: Use the rules for sums of powers of integers to compute the sum. 16 Σ k k=7

A:

Q: 2. Prove that the number of irreducible fractions not greater than 1 and with denominator equal to n…

A: For the solution of the problem follow the next step.

Q: Use ibn al-Haytham's procedure to derive the formula for the sum of the fifth powers of the…

A: We have to derive the formula 15+25+......+n5=n66+n52+5n412−n212 by using ibn al-Haytham's method…

Q: . Show that n! > 3ª for n> 7.

A:

Q: Use the rules for sums of powers of integers to compute the sum. 19 Σ 4.² k=6

A:

Q: (b) Generalize: if the numbers 1 to n are placed around a circle in some order, what is the best…

A: (b) If the numbers 1 to n are placed around the circle in some order, the best possible lower bound…

Q: For all integers n, if n2 is odd then n is odd.

A:

Q: Find the sum of all positive odd integers from 1 to 1239: 1+3+5+7+...+ 1239.

A:

Q: 8. Find the sum of all integers between 20 and 29, including these.

A:

Q: What is the summation from n = 1 to infinity, of  (3n+1) / (5n + 4) ?

A:

Q: The 5th term of an A.P. is 15 and the first term is 3. What is the sum of the first 10 terms?

A:

Q: 16. What is the greatest integer N such that (10 – N) + (16 - N)> 5?

A:

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

A:

Q: FIND THE SMALLEST n So THAT I

A: In this question, we have to find n for given |Rn|<0.0001.

Q: For how many positive integers 'n', n3-8n2 + 20n - 13 is a prime?

A: Introduction :

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

A:

Q: Use the rules for sums of powers of integers to compute the sum. 18 Σ; j=5

A: We can find the answer in the following steps.

Q: 5. Find the sum of all the odd integers from 100 to 200, inclusive. a. 7,000 b. 7,500 6. How many…

A:

Q: Use the rules for sums of powers of integers to compute the sum. 22 [² j=8

A:

Q: 2. What are the two largest positive integers n satisfying n - 1 | n²-A?

A:

Q: Use the rules for sums of powers of integers to compute the sum. 21 Σ k k=3

A:

Q: what is the sum from k=1 to k=infinity of 2k/(k+7k)?

A: To determine the sum.

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

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

Q: Use the rules for sums of powers of integers to compute the sum. 24 4.² k=8

A: Recall: sum of squares of n integer                    ∑i=1ni2=n(n+1)(2n+1)6

Q: that if 3 divides the sum of the digits of n, then 3|n

A:

Q: 3.) An airplane takes off and then climbs 2600 feet. After 25 minutes, it descends 150 feet. What is…

A: Please note that as per our guidelines if multiple questions are posted, we can answer the first…

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

A:

Q: Compute the indicated sums. 8 k=1 8 (k – 1)? =] k=1

A: We will solve the sums.

Q: Show that n! > 3ª for n > 7.

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

Q: 3. Determine the nth-term formula for the number of square tiles in the nth figure. а. a2 a4 as b.…

A:

Q: Prove Γ (n) = (n-1)! where n ∈ ℕ

A: Concept: The proof for this gamma integral will be done using mathematical induction

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: #1. Compute the sum, if po 8 n 3 () 5 n=0

A: It's a GP with infinite terms and having common ratio between -1 and 1

Q: The ratio of the sums of m and n terms of an AP is m2 : n2.show that the ratio of the mth and nth…

A:

Q: How many different ways could you choose any 4 gumballs from the 25 gumballs in the…

A: We can choose 4 gumballs from the 25 gumballs in 25C4 ways.

Q: Use the approach in Gauss's Problem to find the following sums of arithmetic sequences.…

A:

Q: The sum of the digits in the number 56 is 11. (5+6=11) a) Show that the sum of the digits of the…

A: a) Sum of the digits from 15 to 18 1+5=6 1+6=7 1+7=8 1+8=9 Now 6+7+8+9=30

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: If n is 0 what is 8n

A:

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: Find σ(n) if n = 2^k-1 (2^k - 3) where 2^k - 3 is prime

A:

Q: This is a discrete math question: Discover and prove a formula for the sum of the first n odd…

A:

Q: If n is an even integer then 7-n3 is sometimes even and sometimes odd. O is an odd integer is an…

A: We have to state whether the 7-n3 is an even integer, odd integer, or sometimes even and sometimes…

Q: How many corresponding integers are made up of 1443 digits taken from (1-2-3-4-5-6) provided that no…

A:

Q: -Findthe Sum of the first 500 positive, odd integers.

A:

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.