0Addition 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.
