THE GREAT GAUSSIAN SUMMATION TRICK

   

                                              
 

One of the most famous mathematicians of all times was named Karl Gauss. One day, as the story goes, his teacher gave the class an assignment to keep them busy so that he could take a nap in the back of the class. The problem he assigned would keep most of us busy for at least a half an hour, if not more. However, to his teacher's surprise, young Mr. Gauss solved it in seconds. Here is the problem the teacher assigned. Students were told to add all the whole numbers from one to one hundred. That is, 1+2+3+4+5 …98+99+100. In less time than it took most students to write out this one hundred number addition problem, Gauss got the answer. The sum is 5,050 he told his teacher confidently, and so it was.  

But how did he arrive at this answer in so short a time?

Gauss was a genius, and geniuses sometimes see things differently than most of us non genius types. But that doesn't mean that after being shown the way that we cannot solve a problem like a genius would, having first been shown the way.Here is how young Gauss arrived at his answer so quickly. He observed that in the series of numbers 1 +2 + 3 +4 …97 + 98+ 99 + 100, the sum of pairs of numbers from each end, and working in toward the middle summed to the same value, 101.

In other words, 1 + 100, 2 +99, 3 + 98, 4 + 97 etc. all sum to 101! Since there are fifty pair of numbers in the series 1 to 100, Gauss reasoned that the sum of all the numbers would be 50 times 101 or 5,050.

SHERAN EKANAYAKA
2012/2013