The number e is irrational as it cannot be written as a ratio of two integers. Its approximated value is 2.72. That is, e ≈ 2.72. So e is an irrational number between 2 and 3. The number e is regarded as a mathematical constant (known as Euler’s number or Napier’s constant). Also, e is … Read more
The product of three consecutive integers is divisible by 6. That is, for an integer n, the product n(n+1)(n+1) is always divisible by 6. Prove that the Product of 3 consecutive integers is divisible by 6 By division algorithm, every integer when divided by 3 leaves the remainder 0, 1, or 2. So an integer … Read more
The square of an odd integer is of the form 8n+1 where n is an integer. That is, If m is an odd integer then m2 =8n+1 for some integer n. Prove that the square of an odd integer is of the form 8n+1. Answer: By division algorithm, when we divide an integer by 4 … Read more
The number 3/2 in words, that is, 3/2 is spelled out as three halves (or, one and a half). 3/2 is neither an integer or a whole number, it is a rational number. Is 3/2 an Integer Answer: No, the number 3/2 is not an integer. Explanation: We know that $\dfrac{3}{2}=1 \dfrac{1}{2}$. In decimal form, … Read more
We will learn about opposite numbers in this post. The two operations addition and subtraction are involved in the concept behind opposite numbers. Let’s learn what are opposite numbers. Definition of Opposite Numbers A number is called the opposite number of a given number if their sum is zero. More precisely, m is called the … Read more
Numbers are not only a crucial part of mathematics but also play a vital role in our everyday life to count things. Numbers (more specifically integers) are classified into even and odd numbers. In this section, we will learn them together. If you are interested to know them separately then visit our pages below: Even … Read more
Numbers are very useful in our daily life to count many things. By the divisibility rule of 2, we can classify numbers (integers) as follows: even numbers and odd numbers. Note that even numbers are completely divisible by 2 whereas odd numbers are not divisible by 2 that leaves the remainder 1. In this section, … Read more
Numbers play a very crucial role in the world of mathematics, even in our daily life to count things. Note that 4 can be divided into two equal parts, but 5 cannot. Here 4 is an even number, but 5 is not. So we can say that numbers have types. There are two types of … Read more
In this section, we will discuss the formulas of the sum of the squares of natural numbers. These formulas are very useful in various competitive exams. Sum of squares of first n natural numbers: The sum of squares of consecutive natural numbers is determined by the formula below: Prove that:$1^2+2^2+3^2+\cdots+n^2$ $=\dfrac{n(n+1)(2n+1)}{6}$ Proof: Let $S$ denote … Read more