In the geometric series given by the summation \( \sum_{n=1}^{10} (100)(2)^{n-1} \), the range of \( n \) is from 1 to 10.
This means there are a total of 10 terms in the series, since the series sums from \( n = 1 \) to \( n = 10 \).
Thus, the number of terms is 10.