(x+1)+(x+2)+(x+3).........(x+1000)
=x+1+x+2+...+x+1000
=1000x+(1+2+3+...+1000)
=1000x+(1000-1+1).(1000+1):2=500500+1000x
\(\left(x+1\right)+\left(x+2\right)+\left(x+3\right)+...+\left(x+1000\right)\)
\(=\left(x+x+x+...+x\right)+\left(1+2+3...+1000\right)\)
= \(1000x+500500\)