Let an be the nth term of the G.P. of positive numbers. Let ∑100n=1a2n=α and ∑100n=1a2n−1=β, such that such that α≠β. Prove that the common ratio of the G.P. is αβ.

Let an be the nth term of the G.P. of positive numbers. Let ∑100n=1a

1.	Let an be the nth term of the G.P. of positive numbers. Let ∑100n=1a2n=α and ∑100n=1a2n−1=β, such that such that α≠β. Prove that the common ratio of the G.P. is αβ.
Answer» Let $a_{n}$ be the $n^{t h}$ term of the G.P. of positive numbers. Let $\sum_{n = 1}^{100} a_{2 n} = α$ and $\sum_{n = 1}^{100} a_{2 n - 1} = β$ , such that such that $α \neq β$ . Prove that the common ratio of the G.P. is $\frac{α}{β}$ .

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Let an be the nth term of the G.P. of positive numbers. Let ∑100n=1a2n=α and ∑100n=1a2n−1=β, such that such that α≠β. Prove that the common ratio of the G.P. is αβ.

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