What is the maximum number of consecutive positive integers that can be added together to create a sum less than 400?

n*(n+1) / 2 =400, solve for n

n = < 28

So, the first 27 counting numbers 1 + 2 + 3 + 4 +..........+ 27 =378. If you add the 28th number, you will get =378 + 28 =406 which is > 400.