Is it a cloth tailor?

We know that n! is an expression that becomes very large, very quickly. Thus, 1/n! would become very small, very quickly.

If we go up to just n = 4, we can get:

1/1 + 1/2 + 1/6 + 1/24 = approximately 1.7

Using some logic, we can deduct that the remaining portion of the summation notation will not increase the current sum by almost 0.8 which would be needed in order to be rounded up to 3.

Thus, the answer is 2.

$\sum_{n=1}^\infty \frac{1}{n!}=e-1\approx{\boxed{2}}$