1) What was the answer?
2) What was the student’s “trick”?
3) Who was the student?
1) 5,050
2) There are 100 integers, 1 through 100. Add the first and last => 1 + 100 = 101. Add the second and second to last => 2 + 99 = 101. Continue the process until the fiftieth and fiftieth to last => 50 + 51 = 101. Therefore we have 50 pairs of 101. 50 x 101 = 5,050. In general to add the integers 1 through n the formula is (n/2)*(n+1) or more commonly written as (n*(n+1))/2. (This works for all n where n can be odd or even.)
3) If I remember correctly the student was Carl Friedrich Gauss who lived in the late 1700s to mid 1800s.
Good night everyone