IN his head, bitchez!
Or in longer words: by noting 1+100=101, 2+99=101, ... , 50+51=101
50 pairs of numbers summing to 101, so 50x101 = 5050
The integers are 99, 100 and 101. There is also a set of consecutive even integers whose sum is 300. That set is 98, 100 and 102.
Gauss' method, supposedly at the age of 5 according to the story ...Consider pairs:1 + 100 = 1012 + 99 = 1013 + 98 = 1014 + 97 = 1015 + 96 = 101Each pair sums to 101, and there are (100/2) = 50 of them.So their grand sum is (101 x 50) = 5050.
Gauss's method was to find the sum of 1-100. He tried adding with pairs 1 + 100 = 101, 2 + 99 = 101 and so on. Each pairs was going to equal 101. Half of 100 is 50, 50 x 101 = 5,050.
99, 100, and 101
They are 13.
The sum of the integers from 1 to 100 inclusive is 5,050.
The formula for calculating the Gauss sum from 1 to 100 is n(n1)/2, where n is the number of terms in the sequence.
101
Gauss was a German mathematician who, as a child prodigy, was able to calculate the sum of all numbers from 1-100 in less then a minute.
Using Gauss's method, 1+2+3...1000= 500x1001=500500 Answer:500500
The sum of the integers from 1 to 100 can be calculated using the formula for the sum of an arithmetic series: ( S_n = \frac{n(n + 1)}{2} ), where ( n ) is the last integer in the series. Here, ( n = 100 ), so the sum is ( S_{100} = \frac{100(100 + 1)}{2} = \frac{100 \times 101}{2} = 5050 ). Therefore, the sum of the integers from 1 to 100 is 5050.
It is 2500.
The integers are 99, 100 and 101. There is also a set of consecutive even integers whose sum is 300. That set is 98, 100 and 102.
They are 2n+2
The sum of all the digits of all the positive integers that are less than 100 is 4,950.
It is 100*(100+1)/2 = 50500.
Gauss' method, supposedly at the age of 5 according to the story ...Consider pairs:1 + 100 = 1012 + 99 = 1013 + 98 = 1014 + 97 = 1015 + 96 = 101Each pair sums to 101, and there are (100/2) = 50 of them.So their grand sum is (101 x 50) = 5050.