# How to Add Consecutive Integers from 1 to 100

A while back a teacher proposed to a young student the following problem. Compute the sum 1+2+3+...+100

## Steps

- 1
**Divide the sequence into two subsequences of half the total number 100/2=50.**- One subsequence is formed by all the natural numbers less than or equal to 50.
- The other subsequence is formed by all the natural numbers greater than 50.

- 2
**Place the first subsequence in natural numerical order 1,2,3, .**..,50 - 3
**Place under the above subsequence the second subsequence but in reverse order.**Begin with 100, 99, 98, ..., 51. - 4
**Add each of the columns of two numbers from the sequence.**The first column is 1+100=101, the second column is 2+99=101, until you get to 50+51=101. - 5
**Since we have 50 numbers as the result of the columns additions and these 50 numbers are 101.**The total number representing the sum is 50*101=5050. - 6
**The sum 1+2+3+ .**..+100=5050

## Article Info

Categories: Algebra