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Question

Question: The sum of first \(n\) natural numbers is....

The sum of first nn natural numbers is.

A

n(n−1)n ( n - 1 )

B

n(n−1)2\frac { n ( n - 1 ) } { 2 }

C

n(n+1)n ( n + 1 )

D

n(n+1)2\frac { n ( n + 1 ) } { 2 }

Answer

n(n+1)2\frac { n ( n + 1 ) } { 2 }

Explanation

Solution

We know that natural numbers are 1,2,3,4,………1,2,3,4 , \ldots \ldots \ldots are in A.P.

Now sum =n2[2×1+(n−1)1]=n2(n+1)= \frac { n } { 2 } [ 2 \times 1 + ( n - 1 ) 1 ] = \frac { n } { 2 } ( n + 1 ).