Write 0 as the sum of 11 consecutive integers?

Answer 1

If we put 0 in the middle and then look for 10 consecutive integers with 5 being positive and then other 5 being the negatives of those, it will equal 0.

So (-5)+(-4)+(-3)+(-2)+(-1)+0+1+2+3+4+5.

It is very easy to see this works by just paring up each number with its additive inverse.

So - 5 and 5 cancel out, 4 and -4 add up to 0 etc. And of course, 0 it the additive identity so it does not change the sum.