Sum to infinity of a geometric is twice the sum of first two terms. Then what are the possible values of the common ratio?
\(\frac{a}{1-r} = 2(a + ar) = 2a(1 + r)\)
\(1 = 2(1 - r)(1 + r) = 2(1 - r^2) \Rightarrow r^2 = \frac{1}{2}\)
\(r = \pm\frac{1}{\sqrt{2}}\) (both satisfy \(|r| < 1\))
Answer: (A)
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