Let the GP is a , ar , ar² , ar³ , .......... arⁿ⁻¹.

S = Sum of n terms

= a + ar + ar² + ar³ + .......+ arⁿ⁻¹

and R = sum of reciprocal of n terms

P = product of n terms = a × ar × ar² × ar³ × .....× arⁿ⁻¹

=(a¹⁺¹⁺¹⁺¹⁺¹⁺¹⁺¹⁺⁻⁻¹)(r¹⁺²⁺³⁺⁻⁻⁻⁻⁽ⁿ⁻¹⁾〉

take square both sides,

⇒

⇒

⇒

Thus,

⇒