Answer :

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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