Let an be the nth term of the G.P. of positive numbers. Let 
and 
such that α ≠ β. Prove that the common ratio of the G.P. is α /β
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.
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