1 ]   There are twos, threes and five each being  8  in number. Find the

       sum of  the products of these numbers taking at least one  2,3, and  5.

 

2]    The first term of an infinitly decreasing  GP  is unity and its sum is  S.

       Find the sum of the squares of the terms of the progression.

 

3 ]  An  AP  and an  HP have the same first term, the same last term and the same number of terms. Prove that the product of the rth term from the beginning of the first sequence and the rth term from the end of the second sequence is independent of  r.

 

 

4 ]  Find the sum of the product of the integers  1,2,3........, n  taken two at a time and show that it is equal to half the excess of the sum of the cubes of the given integers over the sum of their squares.