Another Way to Approximate the Value Of $e$ Is Through the Sum

Multiple Choice

Another way to approximate the value of $e$ is through the sum $1+\frac{1}{1 !}+\frac{1}{2 !}+\frac{1}{3 !}+\ldots$ . The notation $n !$ represents $n$ factorial, which is the product of all the integers from 1 through $n$ . The more terms added to the sum, the closer the sum gets to e. In calculus, we say that the limit of this sum is e. Find the sum of the first $k$ terms, rounded to the nearest hundred-thousandth, and determine how close the result is to e rounded to the nearest hundred-thousandth (2.71828) .
- $\mathrm{k}=5$ terms

A) $2.71828,0$
B) $2.71667,0.00161$
C) $2.70833,0.00995$
D) $2.5,0.21828$