In the presented work, teachers of higher educational institutions are offered one method of presenting the topic "Number series and its convergence". In most textbooks on mathematical analysis and higher mathematics intended for students of higher educational institutions, the definition of a number series is often given in the following formulations: “A number series is an infinite sum of numbers in a number sequence” or “A number series is an expression made up of numbers in a number sequence”, from who do not understand the meaning of the number series.

In the article, the presentation of the topic is proposed to begin with a study of the problem of extending the concept of the sum of numbers, inherent, so far, only for several numbers, to the numbers of a given sequence and ways to solve it. Then, it is proposed to introduce the concept of a number series, as a number sequence, considered from the position of summing its numbers with an explanation why the numbers of the sequence are not called terms, as in the case of summing several numbers. The authors believe that the presentation of the topic in this sequence fully reveals the essence of the topic.