Mayli, keling, \(L\) bilan tanishish uchun nisbat testidan boshlaylik.

\[\begin{align*}L & = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{\left( {n + 2} \right){{\left( {x - 2} \right)}^{n + 1}}}}{{\left( {2n + 3} \right)!}}\frac{{\left( {2n + 1} \right)!}}{{\left( {n + 1} \right){{\left( {x - 2} \right)}^n}}}} \right| = \mathop {\lim }\limits_{n \to \infty } \left| {\frac{{\left( {n + 2} \right)\left( {x - 2} \right)}}{{\left( {2n + 3} \right)\left( {2n + 2} \right)\left( {2n + 1} \right)!}}\frac{{\left( {2n + 1} \right)!}}{{\left( {n + 1} \right)}}} \right|\\ & = \left| {x - 2} \right|\mathop {\lim }\limits_{n \to \infty } \frac{{n + 2}}{{\left( {2n + 3} \right)\left( {2n + 2} \right)\left( {n + 1} \right)}} = 0\end{align*}\]

OK, biz buni ko'rishimiz mumkin, bu holda, har bir \(x\) uchun \(L = 0\).

2-qadam

Shuning uchun biz yaqinlashuv oralig'i \(\require{bbox} \bbox[2pt,border:1px solid black]{{ - \infty < x < \infty }}\) va yaqinlashish radiusi \(\require{bbox} \bbox[2pt,border:1px solid black]{{R = \infty }}\) ekanligini bilamiz.