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

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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