In this article we will learn some shortcuts to add, if a series of odd number or even numbers are provided. For example in an examination it is asked, add all the ever numbers between 1 to 50 and then add all the odd numbers between 1 to 100 and then add both the results to get an answer. The trick to solve such kind of problems is

There are 25 even numbers between 1 and 50, the addition of all 25 even numbers can be calculated as multiplying amount of even numbers in the range to amount of odd number +1, in this case it will ( 25 x 26) = 650

The sum of odd numbers can be calculated as square of amount of odd numbers in the range in our case it will be square of 50 or 50 x 50 = 2500. So result of the sum of 2 numbers is 2500 +650 = 3150

As a rule we can say

For Adding Odd Numbers in a range : Square the amount of odd numbers in Series

For Adding Even Numbers in a range: Multiply the amount of even number in series to one more than their number

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