1.If the AM ,GM and HM of the first and last terms of the series 25,26,27,.....N-1,N are the terms of the series,find the value of N?

2.The sum of all possible products of the first 'N' natural numbers taken two bu two is:

a)1/24n(n+1)(n-1)(3n+2)

b)n(n+1)(n-1)(2n+3)/24
c)n(n+1)(n-1)(2n+1)/6

d) none of these

Solution 2) 

As we know that

Hence, the sum of all possible products of the first n natural numbers taken two by two is 


Solution 1) 


 

therefore, according  to the statement , 

  • 27
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