Opposite Numbers: Definition, Examples, Properties, and Problems

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

Divisors of 32

The divisors of 32 are those numbers that completely divide 32 without a remainder. In this section, we will discuss about divisors of 32. Highlights of Divisors of 32 Divisors of 32: 1, 2, 4, 8, 16 and 32 Negative divisors of 32: -1, -2, -4, -8, -16 and -32 Prime divisors of 32: 2  Number of divisors … Read more

Factors of 51

Definition of factors of 51: If a number completely divides 51 with the remainder zero, then that number is called a factor of 51. By the above definition, we can say that the factors of 51 are the divisors of 51. In this section, we will learn about the factors of 51 and the prime … Read more

Factors of 26

If a number completely divides 26 with the remainder zero, then that number is called a factor of 26. So we can say that the factors of 26 are the divisors of 26. In this section, we will learn about the factors of 26 and the prime factors of 26. Also Read: Basic concepts of factors … Read more

Sum of cubes of natural numbers

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 cubes of first n natural numbers: We determine the sum of cubes of consecutive natural numbers by the following formula: Prove that:$1^3+2^3+3^3+\cdots+n^3$ $=[\frac{n(n+1)}{2}]^2$ Proof: Let $S$ denote … Read more

Hello world!

Welcome to Mathstoon!       Problem 1: Evaluate $\int e^{2x} \,dx$ Solution: Let $2x=t$. $\int \frac{\tan x}{\cot x} dx$ $=\int \tan^2 x \ dx$ $= \int (\sec^2 x-1)\ dx$   Problem 2: Show that $\log_3 \log_2 8=1$ Solution: At first, we calculate $\log_2 8$. Now, $\log_2 8=\log_2 2^3$ $=3 \log_2 2 \quad$ \$[\because … Read more