Числовые знакопеременные ряды

\[ \newcommand{\const}{\mathrm{const}}\newcommand{\M}{\mathrm{M}}\newcommand{\D}{\mathrm{D}}\newcommand{\p}{\mathrm{P}} \newcommand{\Q}{\mathbb{Q}}\newcommand{\R}{\mathbb{R}}\newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}}\newcommand{\sfrac}[2]{\frac{#1}{#2}} \DeclareMathOperator{\tg}{tg}\DeclareMathOperator{\arctg}{arctg}\DeclareMathOperator{\sign}{sign} \DeclareMathOperator{\sh}{sh}\DeclareMathOperator{\ch}{ch} \newcommand{\simc}{\overset{\text{сх-ти}}{\sim}} \]