If we have a series starting at 1 and we keep adding half of the previous term and take an infinite amount of terms
$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...$$
I understand how we can say that the limit of the sum of this series approaches 2 (as I can make the sum as close to two as I want by taking at least $n$ number of terms), but is it correct to say that
$$1+\frac{1}{2}+\frac{1}{4}+\frac{1}{8}+\frac{1}{16}+...=2$$
And if yes, how can this be? After all, if I continue to keep taking half of the remaining distance between the sum and 2, even when the distance becomes infinitesimally small, I will still not arrive at 2...