1. The problem asks to find the sum of the arithmetic progression (AP) series starting from 80, 81, 82, ..., up to 139, 140 which are 100 positive integers. 2. First, let's identify the first term $a_1=80$ and the last term $a_n=140$. 3. The number of terms $n=100$ is given. 4. The formula for the sum of an AP series is $$S_n=\frac{n}{2}(a_1 + a_n)$$ 5. Substitute the values: $$S_{100} = \frac{100}{2} (80 + 140)$$ 6. Simplify inside the parentheses: $$80 + 140 = 220$$ 7. Now calculate the sum: $$S_{100} = 50 \times 220 = 11000$$ 8. So, the sum of these 100 positive integers in the series is $11000$.