Legend has it that the great mathematician carl friedrich gauss ​(1777dash–​1855) at a very young age was told by his teacher to find the sum of the first 100 counting numbers. while his classmates toiled at the​ problem, carl simply wrote down a single number and handed the correct answer in to his teacher. the young carl explained that he observed that there were 50 pairs of numbers that each added up to 101. so the sum of all the numbers must be 50 times •101equals=5050. modify the procedure of gauss to find the sum. 1plus+2plus+3plus+...plus+375375
S=1+2+3+...+375,375 Â Â Excluding the final term, there are 375,374/2 pairs of numbers that each adds up to 375375. Â Â Â Â Therefore,
S = (375,374/2)*375,375+375,375 =70,453,383,000
