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Mathematics

The sum of first n natural numbers is:

  1. n(n1)2\dfrac{n(n − 1)}{2}

  2. n(n+1)2\dfrac{n(n + 1)}{2}

  3. n(n+2)2\dfrac{n(n + 2)}{2}

  4. n(n2)2\dfrac{n(n − 2)}{2}

AP

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Answer

The sequence of natural numbers 1, 2, 3,….., n.

a = 1

l = n

no. of terms = n

Sum of n terms of an A.P. is given by,

∴ Sn = n2\dfrac{n}{2} (a + l)

= n2\dfrac{n}{2} (1 + n)

= n(n+1)2\dfrac{n(n + 1)}{2}

Hence, option 2 is the correct option.

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