how do you add together all the number's up to 100, Quickly though.
5050
formula
sum of sequence of numbers=(n/2)(first number plus last number)
n is total amount of digits
so total = (100/2)(1+100)
=50(101)
=5050
To get the formula, you need to do what Gauss did as a child. He paired the numbers up, reading from both ends:
1+2+3+4+...+97+98+99+100
is the same as
(1+100) + (2+99) + (3+98) + (4+97) + ... + (50+51)
There are 100 numbers, so there are 50 pairs adding to 101
sum = 101*100/2
To add together all the numbers up to 100 quickly, you can use a mathematical formula called the sum of an arithmetic series. The formula for the sum of an arithmetic series is:
Sum = n/2 * (first term + last term)
In this case, the first term is 1 and the last term is 100. We need to find the number of terms, which we can do by simply counting the numbers from 1 to 100.
n = 100 - 1 + 1 = 100
Now, plug the values into the formula:
Sum = 100/2 * (1 + 100)
= 50 * 101
= 5,050
Therefore, by using the formula, the sum of all the numbers up to 100 is 5,050.