Legend has it that the great mathematician Carl Friedrich Gauss (1777–1855) at a very yo...

Legend has it that the great mathematician Carl Friedrich Gauss (1777–1855) 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. (See below.) So the sum of all the numbers must be 50 × 101 = 5050.

Use the method of Gauss to find each sum.

1 + 2 + 3 + ⋅⋅⋅ + 200