Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P.

Question

Let S be the sum, P the product and R the sum of reciprocals of n terms in a G.P. Prove that P 2 R n = S n .

Philoid · Accepted Answer

Let the G.P. be a, ar, ar², ar³, … ar^{n - 1}…

According to question -

[∵ Sum of first n natural numbers is n(n + 1)/2]

Now,

L.H.S = P²Rⁿ

= Sⁿ

= R.H.S

Hence, P²Rⁿ= Sⁿ