As you may know, the sum of the first 100 whole numbers can be
solved from this formula 
but if you were a primary school student how would you solve this question without any formula?
1+2+3+4+5+6+7+......+100
in primary school, after the young Gauss misbehaved, his teacher, J.G. Büttner, gave him a task: add a list of integers in arithmetic progression; as the story is most often told, these were the numbers from 1 to 100. The young Gauss reputedly produced the correct answer within seconds, to the astonishment of his teacher and his assistant Martin Bartels(Wikipedia)
Ok. Can you repeat history and solve the question? Can you really solve
it without using formulas?
I will post the answer next time.
if I see that you enjoy these questions I may post more interesting math questions like this.