Question

The sum of first n
natural numbers is [MP PET 1984; RPET 1995]
A) n\,(n-1) B) \frac{n\,(n-1)}{2} C) n\,(n+1) D) \frac{n\,(n+1)}{2}

Answer 1

Hey mate !!

Here's your answer !!

We know that sum of terms of an AP has a formula as:

$S_{n} = n / 2 * [ 2a + ( n - 1 ) d ]$

So let's write the AP for the the natural numbers.

AP = 1, 2, 3, 4, 5 ......∞

Here,

a = 1

d = 1

n = n 

So, The sum is as follows:

$S_{n} = n / 2 * [ 2 ( 1 ) + ( n - 1 ) * 1 ]$

[tex] S_{n} = n / 2 * [ 2 + n - 1 ] [/tex]

$S_{n} = n / 2 * ( n + 1 )$

[tex]= S_{n} = n ( n + 1 ) / 2 = S_{n} = n^{2} + n /2 [/tex]

Hope my answer helped !!

Cheers !!