Answer
$n=5000$
Work Step by Step
Recall the formula that $\text{Error}=|R_n| \leq a_{n+1}$
Here, we have
$R_n \leq \dfrac{1}{2n+1} \lt 10^4$
and $ \dfrac{1}{2n+1} \lt 10^{-4}$
or, $2n+1 \gt 10^4$
or, $n \gt 5000-0.5$
or, $n \gt 4999.5$
or, $n=5000$
