Compute 1 + 2 + 3+ ... + 98 + 99 + 100.

Answer 1

well, lets see what we can do with 5
1 2 3 4 5
3 is in the middle
3*5 = 15 that works
lets try 6
1 2 3 4 5 6
3 1/2 is in the middle
3 1/2 * 6 = 21
sure enough that is 15 + 6
lets try 10
1 2 3 4 5 6 7 8 9 10
5 1/2 * 10 = 55
is that 21 + 7 + 8 + 9 + 10? YES !
so
I think
55 * 100 = 5,500

Answer 2

100*101/2 = 5050