Answer: The difference between sum of first 20032003 even numbers and sum of first 20032003 odd numbers is “-20032003”.
Step-by-step explanation:
The sum of first 20032003 even numbers:
![Summation E=E_{1}+E_{2}+E_{3}+ . . . . . +E_{20032003}](https://tex.z-dn.net/?f=Summation%20E%3DE_%7B1%7D%2BE_%7B2%7D%2BE_%7B3%7D%2B%20.%20.%20.%20.%20.%20%2BE_%7B20032003%7D)
The sum of first 20032003 odd numbers:
![Summation O=O_{1}+O_{2}+O_{3}+ . . . . . +O_{20032003}](https://tex.z-dn.net/?f=Summation%20O%3DO_%7B1%7D%2BO_%7B2%7D%2BO_%7B3%7D%2B%20.%20.%20.%20.%20.%20%2BO_%7B20032003%7D)
Difference between the sum of first 20032003 even numbers and the sum of first 20032003 odd numbers:
![Difference=Summation E - Summation O=(E_{1}+E_{2}+E_{3}+ . . . . . . . +E_{20032003})-(O_{1}+O_{2}+O_{3}+ . . . . . . . +O_{20032003})](https://tex.z-dn.net/?f=Difference%3DSummation%20E%20-%20Summation%20O%3D%28E_%7B1%7D%2BE_%7B2%7D%2BE_%7B3%7D%2B%20.%20.%20.%20.%20.%20.%20.%20%2BE_%7B20032003%7D%29-%28O_%7B1%7D%2BO_%7B2%7D%2BO_%7B3%7D%2B%20.%20.%20.%20.%20.%20.%20.%20%2BO_%7B20032003%7D%29)
![Difference=(E_{1}-O_{1})+(E_{2}-O_{2})+(E_{3}-O_{3})+ . . . . . . . +(E_{20032003}-O_{20032003})](https://tex.z-dn.net/?f=Difference%3D%28E_%7B1%7D-O_%7B1%7D%29%2B%28E_%7B2%7D-O_%7B2%7D%29%2B%28E_%7B3%7D-O_%7B3%7D%29%2B%20.%20.%20.%20.%20.%20.%20.%20%2B%28E_%7B20032003%7D-O_%7B20032003%7D%29)
Even numbers start as 0, 2, 4, 6…. While odd numbers start as 1, 3, 5, 7…..
(assuming that we are taking non-negative even/odd numbers into account only)
As we know, every nth even number is one behind their respective odd number (i.e. 0 lags 1, 2 lags 3, 4 lags 5 and so on)
Thus, our equation of difference becomes,
![Difference=(-1)_{1}+(-1)_{2}+(-1)_{3}+ . . . . . . . +(-1)_{20032003} =(-1)*20032003=-20032003](https://tex.z-dn.net/?f=Difference%3D%28-1%29_%7B1%7D%2B%28-1%29_%7B2%7D%2B%28-1%29_%7B3%7D%2B%20.%20.%20.%20.%20.%20.%20.%20%2B%28-1%29_%7B20032003%7D%20%3D%28-1%29%2A20032003%3D-20032003)
Learn more about even & odd numbers here brainly.com/question/24657250
#SPJ4