What is the sum of the first 10 odd positive integers?
The first 10 positive odd integers are 1, 3, $\dots$, 19.  The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum of the first 10 positive odd integers is \[\frac{1 + 19}{2} \cdot 10 = \boxed{100}.\]