Sum of first n natural numbers formula and derivation

Learn how to find sum of first n natural numbers. Here am going to give information about the method for finding n natural numbers sum. 

Learn how to find sum of first n natural numbers. Here am going to give information about the method for finding n natural numbers sum.

Derivation of Formula for finding sum of n natural numbers:

Let

      sn = sum of n terms

       n = number of terms

sn=   1 +    2 +       3 +        4 +        5 +……………………+ (n-4) + (n-3) + (n-2) + (n-1) + n    eq 1

sn=   n + (n-1) + (n-2) + (n-3) + (n-4)……………    ……    +5 +     4    +    3    +     2   + 1     eq 2

Add eq 1 and 2

We get

2 sn = (n+1) + (n+1) + (n+1) + (n+1) + (n+1) +………………..+ (n+1) + (n+1) + (n+1) + (n+1) + (n+1) 

2 sn = n ×  ( n+1)                             (  we are adding ( n+1)   n times)

sn = n (n+1)2  

 

Examples on sum of first n natural numbers:

  1. Find the sum of first 100 natural numbers.

Solution:

                    sn = n (n+1)2  

                       = 100 ( 100+1)2 

                        = 50 × 101

                         = 5050

 

2. Find the sum of first 50 natural numbers?

Solution:

                    sn = n (n+1)2  

                      = 50 ( 50+1)2 

                      = 25 × 51

                      = 1275

 

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