2.10.126 Number series

Condition: Calculate the sum of a given number series using the Leibniz criterion with an accuracy of at least \( 10^{-4} \) : \[ \frac{1}{14}+\frac{1}{12}-\frac{1}{23}-\frac{1}{20}+\fr ac{1}{36}+\frac{1}{32}-\frac{1}{53}-\frac{1}{48}+\cdots . \]