Problem was in the form of (not the actual problem since I'm not looking for an exact answer)
the series: $3(-1)^n / n!$, how many terms do we need to add to get an error of $10^{-3}$.
While I solved the problem already, it seemed unconventional and I figured out it would be better to find the amount of terms needed.
Generally when solving these problems, we would use a equation to solve for $n$, but I was unsure what to do since there was a factorial.
How would one solve this type of problem?
Best Answer
Same thing as before. The error is less than the last term, so you want $3/n! < .001$ or $n! > 3000 $.
The factorials starting at 4 are 24, 120, 720, 5040, so n=7 has a term of 3/5040 < .001 so 6 terms will do.
What makes this harder is there is no simple inverse function for factorial.