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How to - Find the sum of first 100 natural numbers ?

Find the Sum of first 100 natural numbers 

In this blog we will learn to find the sum of first 100 natural numbers. This type of question is often asked in the competitive exams under Multiple Choice or Short-Answer questions.




The sum of first 100 natural numbers can be calculated using the formula for the sum of an Airthmetic series,

Here, S denotes the Sum of numbers i.e.     

                          S= 1+2+3+4+5+..........n

and n represents the count of natural numbers. Please note that the above formula holds for the sum of first n natural numbers.

In our case, we have first 100 natural numbers. Therefore, value of n will be 100.

Therefore,   S= 1+2+3+4+5+.........................+100

Therefore, sum of first 100 natural numbers is 5050.

Derivation of the formula

Step1: Write down the sequence of first n natural numbers 

                        1+2+3+4+......................................+n

Step2 : Now reverse the order of the sequence

                        n + (n-1)+(n-2)+.................. .........+1

Step3: Add the corresponding terms of both the sequences 


Step4: There are a total of n pairs of (n+1) in the sum, therefore sum is n.(n+1)

Step5: We have counted each number twice, therefore we need to divide the sum by 2.

So, the formula for sum of first n natural numbers is

Another Example :

Find the sum of first 50 natural numbers

Sol. Here, n =50

Therefore, 

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