2.10.126 Number Series

Condition: Calculate the amount of this numerical 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 . \]