Question 259364
The first 1000 consecutive odd numbers run from 1 to 1999. 
The first 1000 consecutive even numbers run from 2 to 2000. 
The sum of numbers from 1 to 2000 is,
{{{N=(2000)(2001)/2=2001000}}}
Each even number is 1 greater than each odd number like 
1, 2
3, 4
Each even number is an odd number plus one. 
So then the total sum is the sum of all the odds twice plus 1000.
{{{2*OS+1000=2001000}}}
{{{2*OS=2000000}}}
{{{OS=1000000}}}
{{{ES=1001000}}}
where OS is odds summed from 1 to 1999 and ES is the evens summed from 2 to 2000.