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Permutations And Combinations
If S1, S2, S3 ........Sp are the sums of n terms of p A.P.’s whose first terms are 1, 2,3, .....p and common differences are 1, 3, 5, .....(2p – 1) respectively. Show that
Here, = Sum of first n terms of an A.P. with first term 1 and c.d. 1.
=
Sum of first n terms of an A.P. with first term 2 and c.d. 3.
=
= Sum of first n terms of an A.P. with first term 3 and c.d. 5.
=
.............................................
..............................................
Sum of first n terms of an A.P. with first term p and c.d. (2p - 1)
∴ =
=
=
=
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