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Geometric series are a fundamental concept in mathematics, frequently encountered in various fields, including calculus, finance, and physics. A such series is a sequence of terms where each term is obtained by multiplying the previous term by a constant ratio. In this article, we will delve into the properties of geometric series, discuss their convergence … Read more

The harmonic series is a widely studied mathematical series that arises from the harmonic sequence, which consists of the reciprocals of positive integers. In this article, we will explore the properties of this series, discuss its convergence behavior, examine its divergent nature, and shed light on its mathematical significance. Definition and Form of the Harmonic … Read more

For several mathematical models, one generally needs to study the limits at infinity of the solution. It is a kind of stability of systems. We then recall this concept and give some examples. We already discussed the limits at the finite points of functions. Now we discuss the case of infinite points. Definitions and properties … Read more

Any uniformly continuous function is actually a continuous function. However, as we will see below, the converse is not true. This important class of functions satisfies useful properties. In this article, we will discuss all these facts in detail. The uniform continuity of a function In some mathematical problems, continuity is not enough to make … Read more

We provide all necessary properties of functions of one variable such as limit at a given point, continuity, and differentiability. Such functions are defined over a domain of the set of real numbers. Continuity of functions of one variable We denote by $\mathbb{R}$ the set of real numbers. If $f$ is a real function, then … Read more

One of the most fundamental theorems in mathematical analysis is the mean value theorem. Geometrically, the theorem says that somewhere between points A and B on a differentiable curve there is at least one tangent line parallel to the secant line AB. Let’s discover together this great theorem and give it some applications. Here will … Read more

The Ratio Test stands as one of the powerful tools at our disposal for investigating the convergence behavior of series. By examining the ratio of consecutive terms, the Ratio Test allows us to make conclusive statements about the convergence or divergence of a series. In this article, we will explore the Ratio Test, discuss its … Read more

The main purpose of this article is to provide examples of convergent series. We also speak of divergent series. Before that, we first give a concise summary of the properties of the series and recall the convergence criteria of the series with the proofs. In fact, to fully understand the contents of this page, information … Read more

We provide you with all details about the geometric sequence. In fact, this simple sequence appears frequently in many subjects such as series and probability. Let us discover together this magic sequence. What is a geometric sequence? Let $a$ be a real number, we denote $a\in\mathbb{R},$ where $\mathbb{R}$ is the set of real numbers. A … Read more