Question

what is the sum of 1 to 100​

Answer 1

Step-by-step explanation: Gauss noticed that if he was to split the numbers into two groups (1 to 50 and 51 to 100), he could add them together vertically to get a sum of 101. Gauss realized then that his final total would be 50(101) = 5050.

Because each of these pairs of numbers adds up to 101. And since there are 50 such pairs, we can very quickly figure out—without doing all 100 addition problems—that the sum of the first 100 positive integers is 50 x 101 = 5,050.