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Permutations And Combinations
Let S be the sum, P the product and R the sum of the reciprocals of n terms in a G.P. Prove that
Let a be the first term and r be the common ratio of a G.P.
S = the sum of n terms of G.P. = a + ar + .........ar^{n1}
∴ ...(i)
P = the product of n terms of G.P. = a. ar. ar^{2} ....... ar^{n1}
∴ P =
...(ii)
R = the sum of the reciprocals of n terms of G.P. =
=
Now,
L.H.S. =
R.H.S. =
∴ L.H.S. = R.H.S.
Hence,
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