The sum of the integers from 1 to 100 is 5050.
This is a classic problem in mathematics that can be solved efficiently using the concept of arithmetic progressions. The sequence 1, 2, 3, ..., 100 forms an arithmetic progression where the first term (a) is 1, the last term (l) is 100, and the number of terms (n) is 100.
The formula to calculate the sum (S) of an arithmetic progression is:
S = (n/2) * (a + l)
In this case:
S = (100/2) (1 + 100)
S = 50 101
S = 5050
Therefore, the sum of the integers from 1 to 100 is indeed 5050. This result is often attributed to Carl Friedrich Gauss, who reportedly found this method as a child.
