There are 500 even numbers from 1 to 1000 starting with 2 and ending with 998. The sequence of even numbers is an arithmetic sequence with a common difference of 2. Using the equation for the arithmetic series,
S = (a1 + an)(n/2)
and substituting,
S = (2 + 998)(500/2)
we get,
S = 250,000
Therefore, the sum of all even numbers between 1 and 1000 is 250,000.
