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 mean of the first 100 integers can be calculated by finding the sum of these integers and dividing by the total count. The sum of the first 100 integers (from 1 to 100) is ( \frac{100(100 + 1)}{2} = 5050 ). Dividing this by 100 gives a mean of ( \frac{5050}{100} = 50.5 ). Therefore, the mean of the first 100 integers is 50.5.
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.
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.
It is 2500.
The sum of all the digits of all the positive integers that are less than 100 is 4,950.
They are 2n+2
It is 100*(100+1)/2 = 50500.