Example 2. Put a positive or negative sign in front of each of the numbers $1,2,3,4, \cdots, 1985,1986$ 
one thousand nine hundred and eighty-six numbers, and ask whether the sum obtained is odd or even?
This problem seems intractable at first glance, because we do not know which numbers should have a positive sign and which should have a negative sign in front of them, and different signs can lead to different results. However, we are only concerned with the parity of the final result. Since the sum and difference of two integers have the same parity, to determine the final result's parity, we can simply add all these numbers with positive signs. Since $1+2$ $+3+\cdots+1986$ includes 993 even addends and 993 odd addends, their sum will be odd, meaning the sum of the 1095 numbers in the problem will also be odd.