Answer:
The answer is "[tex]n \geq 9[/tex] and [tex]error < 10^{-4}[/tex]".
Step-by-step explanation:
[tex]\sum_{n=1}^{\infty} \frac{-1^n}{n 2^n}\\\\[/tex]
Error after [tex]n^{th}[/tex]term:
[tex]|R_n|= |\frac{(-1)^{n+1}}{(n+1) 2^{n+1}}| = \frac{1}{(n+1)2^{n+1}}\\\\\to \frac{1}{(n+1)2^{n+1}} < 0.0001\\\\\to 10000< 2^{n+1} (n+1)\\\\\to n\geq 9 \ \ \text{satisfies the inequality}\\\\\to error< 10^{-4}\\[/tex]
