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 ,