Ishora almashinuvchi qatorlarga doir taqdimot tayyorlash

Preparation of presentation on alternating series. Alternating series in mathematics belong to the series type where the elements of the series change from positive to negative consecutively. Typically, such series are in the form $\sum_{n=1}^{\infty} (-1)^{n+1} a_n$, where $a_n > 0$. Alternating series can be summed according to the Ershov theorem: if $\lim_{n \to \infty} a_n = 0$ and $a_n$ decreases alternately, the series converges. One famous example is the Leibniz series, $\sum_{n=1}^{\infty} \frac{(-1)^{n+1}}{n} = \ln 2$. Such series are commonly used in mathematical analysis and calculations