Answer
$10^{-5}$
Work Step by Step
The Alternating Series Estimation Theorem states:
Consider a series $\Sigma a_n$ such that $A_n=(-1)^n B_n$; $B_n \geq 0$ for all $n$
If the following conditions are satisfied, then the series converges:
a) $\lim\limits_{n \to \infty} B_n=0$;
b) $B_n$ is a decreasing sequence.
We have $S_n=a_1-a_2+......+(-1)^{n+1}a_n$
Now, $|S-S_n|=\leq |a_{n+1}|$
So, $|\space Error |=|S-S_4| \leq |a_{4+1}|=|a_5|$
or, $=|(-1)^5 \times \dfrac{1}{10^5}|$
or, $=10^{-5}$
