# Problem 2.

What is greater: the sum of all odd numbers from 1 to 2019 (inclusive) or the sum of all even numbers from 2 to 2018 (inclusive)?
# Solution.

Let's write the specified sums one under the other

$$
\begin{aligned}
& N=1+3+5+\ldots+2017+2019 \\
& K=2+4+6+\ldots+2018
\end{aligned}
$$

The number of addends in the second sum is 2018/2 = 1009.

Olympiad for Schoolchildren "Hope of Energy". Final Stage. Solutions

It is clear that each addend in the second sum is one more than the corresponding addend in the first sum (standing right below it). Therefore, to get $N$ from $K$, we need to subtract one 1009 times and then add the addend +2019 (which has no counterpart in the sum $K$). We get

$$
N=K-1 \cdot 1009+2019=K+1010.
$$

Thus, $N>K$.

Answer: the sum of odd numbers is greater.