Lesson Posted on 11 Jan Mathematical Induction

How To Quickly Add A Series Of Natural Numbers?

Rashmikant Sinha

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Addition of all the Natural Numbers of a series can be easily and quickly arrived at by using the simple formula: Let's take a series of natural numbers, like a+(a+1)+(a+2)+(a+3)+.......+(a+n), where both a & n are natural numbers. The Formula To arrive at the Sum Total of this series is = /2... read more

Addition of all the Natural Numbers of a series can be easily and quickly arrived at by using the simple formula:

Let's take a series of natural numbers, like a+(a+1)+(a+2)+(a+3)+.......+(a+n), where both a & n are natural numbers.

The Formula To arrive at the Sum Total of this series is

= [(a+n)*{(a+n)+1}]/2 - [a*(a+1)]/2

For Example: Find out the sum total of 11+12+13+14+......+88

Here a=11 & n=(88-11)=77

[Since (a+n)=88 & a=11,

Hence n=88-a=88-11=77]

Hence sum total of the above series is,

[(11+77)*{(11+77)+1}]/2 - [11*(11+1)]/2

= [88*89]/2 - [11*12]/2

= 44*89 - 11*6

= 3916 - 66

= 3850.

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