How to calculate 1+2+3+...+99+100 without a calculator?
1+2+3+...+99+100
form pairs in the following way:
= (1+100) + (2+99) + (3+98) + ....
= 101 + 101 + 101 + ...
how many 101's will you have ?
Legend has it that the famous German mathematician Gauss, did this in his head when his teacher assigned it in early grade school as "busy work" to keep the kids quiet.
Thank you!
To calculate the sum of the consecutive numbers from 1 to 100 without using a calculator, you can use a formula for the sum of an arithmetic series.
The formula for the sum of an arithmetic series is:
S = (n/2)(a + l)
where:
S is the sum of the series,
n is the number of terms in the series,
a is the first term, and
l is the last term.
In this case, the first term (a) is 1, the last term (l) is 100, and the number of terms (n) is 100.
Substituting these values into the formula, we get:
S = (100/2)(1 + 100)
Simplifying further:
S = (50)(101)
Now, evaluate the expression:
S = 5050
So, the sum of the consecutive numbers from 1 to 100 is 5050.