What is the series?
Since this is an alternating series, the sum to "N+2" will always lie between the sum to "N" and "N+1". That means that the full sum will lie between the sum to N and N+1. And that means that the error will be no larger than the absolute value of the difference between those two sums which is just the absolute value of the N+ 1 term:
. (I see now that is what Plato just said.)
In order to get the sum correct within 4 decimal places, that is, with error between -0.00005 and 0.00005, you must use N such that