Question

What is the sum of 1+3+5+7+9+....+1993+1995+1997+1999?

Answer 1

Here's a way for you to think of this problem.

1+3+5+7+9+....+1993+1995+1997+1999 =
= (1 + 1999) + (3 + 1997) + (5 + 1995) + (7 + 1993) + ...

Answer 2

If it were 1 + 2 + 3...+n, the sum would be (1/2)(n)(n+1)

Perhaps you can do something with that. Yes,
take that sum and subtract the even ones, 2 + 4 + 6 +...n
and you know that that even sum is twice the sum from 1 to n/2,

So, total sum 1 to n = even sum + odd sum
odd sum = total - even

That should work. 1 + 3 + 5 + = 1+2+3+4+5...- 2+4+...