4 - Finding The Sum of All Even Numbers Starting From 2

Rule: Multiply the amount of numbers in the group by one more than their number

We shall use this rule to find the sum of all even numbers from 1 to 100. Half of the numbers will be even and half will be odd, which means there are 50 even numbers from 1 to 100. Applying the rule,

50 X 51 = 2,550

Thus the sum of all even numbers from 1 to 100 is 2,550. In Short Cut 2 the sum of all the numbers from 1 to 99 is found to be 4, 950; consequently the sum of all numbers from 1 to 100 is 5,050. In Short Cut 3 the sum of all odd numbers from 1 to 100 is found to be 2,500. Our answer for the sum of all the even numbers from 1 to 100 is therefore in agreement.

Sum of all numbers 5,050
Sum of all odd numbers 2,500
Sum of all even numbers 2.550