Question

Find the sum of first n natural number

Answer 1

The natural numbers are 1,2,3,4,... so sum of first n natural numbers as  

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

$S_{n}$ = 1 + 2 + 3 + 4 + ... + n  

As we know that  

$S_{n} = \frac{n}{2}[ 2a + (n-1)d]$  

According to 'n' natural numbers  

first term = a = 1 and common difference = d = 1  

∴ $S_{n} = \frac{n}{2}[ 2 \times 1 + (n-1) \times1]$  

$S_{n} = \frac{n}{2}[ 2 + n-1 ]$  

$S_{n} = \frac{n}{2}[ n + 1 ]$