How can you add 0 - 100 without using a calculator or going 1+2+3+4 and on?
The story goes that Friedrich Gauss, one of the greatest mathematicians that ever lived, was in grade school when the teacher gave the class some "busywork" to do and told them to add
1+2+3+ ... + 98+99+100
little Gauss, looking at the problem for a moment, came up with the answer mentally, to the astonishment of his teacher.
he added the first and last in his head, 1+100 = 101
then adden the second and the second last 2 + 99 = 101
he added the third and the third last 3 + 98 = 101
ahhhhhh.
so there would be 50 of those 101's, right?
and you should be able to do 50 x 101 in your head.
= 5050
Is there a little easier way 'cause I don't like the 101 method maybe 100? :/
gheee!
I guess 0 + 100 = 100
1 + 99 = 100
2 + 98 = 100
but now you don't have an even number of pairs, you have 50 of those plus the 50 sitting in the middle
so
50 x 100 + 50 = 5050
(I think my first method is easier)
No your right that is what I call a mathmatician because if you keep doing that you get 50 100's and 1 50 50x100=5000+50= 5050
Just checking to see who's a mathmatician. YOU! ha ha ha LOL
Now do you think it's easier.
By the way that 100 method written down is called the scroll of 100's
I know my math teacher, Mr. Logslett is quite eccentric (wierd).
He wants to know why not how.
To add numbers from 0 to 100 without using a calculator or manually adding each number one by one, you can use a mathematical formula. In this case, we can utilize the formula for the sum of an arithmetic series.
The sum of an arithmetic series can be found using the following formula:
S = (n/2) * (first term + last term)
where S is the sum of the series, n is the number of terms, and the first and last terms define the range of the series.
In this case, the first term is 0 and the last term is 100. The number of terms can be calculated by simply adding 1 to the range (100 - 0 + 1 = 101).
Using the formula, we can substitute the values and solve for the sum:
S = (101/2) * (0 + 100)
S = 50.5 * 100
S = 5,050
Therefore, the sum of numbers from 0 to 100 is 5,050.