35. Find the sum of all positive odd numbers not exceeding a thousand.
35. We need to find the sum $1+3+$ $+5+\ldots+997+999$. It is clear that this is the sum of the first 500 terms of an arithmetic progression with the first term 1 and common difference 2. Therefore, our sum is

$1 \cdot 500+\frac{500 \cdot 499}{2} \cdot 2=500+500 \cdot 499=$

$$
=500 \cdot 500=250000
$$