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Question

The harmonic mean of sum of first n natural numbers and sum of cubes of first n natural numbers is


  1. n2(n+1)2 / (n2 + n + 2)

  2. n2(n+1)2 / (n2 + n + 1)

  3. n2(n+1)2 / (n2 + 2n+ 3 )

  4. n2(n+1)2 / (n2 + n + 4 )


Solution

The correct option is A

n2(n+1)2 / (n2 + n + 2)


Sum of first n natural numbers = n(n+1)2

Sum of cubes of first n natural numbers = n2(n+1)24

Harmonic mean = (2[n(n+1)2][n2(n+1)24])([n(n+1)2]+[n2(n+1)24])

=n2(n+1)2(n2+n+2)

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