Let a_n

Let a be the first term and r be the common ratio of the G.P.

Given: and

Explanding the summation we get,

a₂ + a₄ + a₆ +………….a₂₀₀ = α

ar + ar³ + ar⁵ +………..+ ar¹⁹⁹ = α

………………..(1)

Also,

a₁ + a₃ + a₅ +………+ a₁₉₉ = β

a + ar² + ar⁴ +…………+ ar¹⁹⁸ = β

………………….(2)

From equation (1) and (2), Dividing them we get,

Hence, Proved.