How to find the sum of all even and odd numbers

Addition is the basic arithmetic operation what we first learn in our school. Use of modern day technology like calculators in all the forms (generic calculators/calculators in mobile or watch) are making us very negligent towards basic and simple arithmetic, days are not far that for even doing 2+2 we need a calculator.

In the series of articles, I am going to refresh you on some of very basic arithmetic shortcuts which will help all of us in day today life. I had demonstrated adding consecutive numbers and adding consecutive numbers starting from 1, in my pervious article http://www.bukisa.com/articles/39961_short-cuts-for-adding-consecutive-numbers

Finding the sum of all even numbers starting form 2

Thumb rule:

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

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

50 x 51 = 2550

Thus the sum of all even numbers from 1 to 100 is 2550.

Finding the sum of odd numbers starting from 1

Thumb rule:

Square the amount of numbers in the series.

To show this, let’s find the sum of all odd numbers from 1 to 100. As said earlier there are half even numbers and half odd number in this series, which means there are 50 odd numbers from 1 to 100. Applying rule

50 x 50 = 2500

Thus the sum of all odd numbers from 1 to 100 is 2500